Including energy harvesting capability in a wireless network is attractive for multiple reasons. First and foremost, powering base stations with renewable resources could significantly reduce their reliance on the traditional energy sources, thus helping in curtailing the carbon footprint. Second, including this capability in wireless devices may help in increasing their lifetime, which is especially critical for devices for which it may not be easy to charge or replace batteries. This will often be the case for a large fraction of sensors that will form the {em digital skin} of an Internet of Things (IoT) ecosystem. Motivated by these factors, this work studies fundamental performance limitations that appear due to the inherent unreliability of energy harvesting when it is used as a primary or secondary source of energy by different elements of the wireless network, such as mobile users, IoT sensors, and/or base stations. The first step taken towards this objective is studying the joint uplink and downlink coverage of radio-frequency (RF) powered cellular-based IoT. Modeling the locations of the IoT devices and the base stations (BSs) using two independent Poisson point processes (PPPs), the joint uplink/downlink coverage probability is derived. The resulting expressions characterize how different system parameters impact coverage performance. Both mathematical expressions and simulation results show how these system parameters should be tuned in order to achieve the performance of the regularly powered IoT (IoT devices are powered by regular batteries). The placement of RF-powered devices close to the RF sources, to harvest more energy, imposes some concerns on the security of the signals transmitted by these RF sources to their intended receivers. Studying this problem is the second step taken in this dissertation towards better understanding of energy harvesting wireless networks. While these secrecy concerns have been recently addressed for the point-to-point link, it received less attention for the more general networks with randomly located transmitters (RF sources) and RF-powered devices, which is the main contribution in the second part of this dissertation. In the last part of this dissertation, we study the stability of solar-powered cellular networks. We use tools from percolation theory to study percolation probability of energy-drained BSs. We study the effect of two system parameters on that metric, namely, the energy arrival rate and the user density. Our results show the existence of a critical value for the ratio of the energy arrival rate to the user density, above which the percolation probability is zero. The next step to further improve the accuracy of the stability analysis is to study the effect of correlation between the battery levels at neighboring BSs. We provide an initial study that captures this correlation. The main insight drawn from our analysis is the existence of an optimal overlapping coverage area for neighboring BSs to serve each other's users when they are energy-drained. / Ph. D. / Renewable energy is a strong potential candidate for powering wireless networks, in order to ensure green, environment-friendly, and self-perpetual wireless networks. In particular, renewable energy gains its importance when cellular coverage is required in off-grid areas where there is no stable resource of energy. In that case, it makes sense to use solar-powered base stations to provide cellular coverage. In fact, solar-powered base stations are deployed already in multiple locations around the globe. However, in order to extend this to a large scale deployment, many fundamental aspects of the performance of such networks needs to be studied. One of these aspects is the stability of solar-powered cellular networks. In this dissertation, we study the stability of such networks by applying probabilistic analysis that leads to a set of useful system-level insights. In particular, we show the existence of a critical value for the energy intensity, above which the system stability is ensured. Another type of wireless networks that will greatly benefit from renewable energy is internet of things (IoT). IoT devices usually require several orders of magnitude lower power compared to the base stations. In addition, they are expected to be massively deployed, often in hard-to-reach locations. This makes it impractical or at least cost inefficient to rely on replacing or recharging batteries in these devices. Among many possible resources of renewable energy, radio frequency (RF) energy harvesting is the strongest candidate for powering IoT devices, due to ubiquity of RF signals even at hard-to-reach places. However, relying on RF signals as the sole resource of energy may affect the overall reliability of the IoT. Hence, rigorous performance analysis of RF-powered IoT networks is required. In this dissertation, we study multiple aspects of the performance of such networks, using tools from probability theory and stochastic geometry. In particular, we provide concrete mathematical expressions that can be used to determine the performance drop resulting from using renewable energy as the sole source of power. One more aspect of the performance of RF-powered IoT is the secrecy of the RF signals used by the IoT devices to harvest energy. The placement of RF-powered devices close to the RF sources, to harvest more energy, imposes some concerns on the security of the signals transmitted by these RF sources to their intended receivers. We study the effect of using secrecy enhancing techniques by the RF sources on the amount of energy harvested by the RF-powered devices. We provide performance comparison of three popular secrecy-enhancing techniques. In particular, we study the scenarios under which each of these techniques outperforms the others in terms of secrecy performance and energy harvesting probability. This material is based upon work supported by the U.S. National Science Foundation (Grant CCF1464293). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the NSF.

Instantaneous and ergodic rates are two of the most commonly used metrics to characterize throughput of wireless networks. Roughly speaking, the former characterizes the rate achievable in a given time slot, whereas the latter is useful in characterizing average rate achievable over a long time period. Clearly, the reality often lies somewhere in between these two extremes. Consequently, in this work, we define and characterize a more realistic N-slot average rate (achievable rate averaged over N time slots). This N-slot average rate metric refines the popular notion of ergodic rate, which is defined under the assumption that a user experiences a complete ensemble of channel and interference conditions in the current session (not always realistic, especially for short-lived sessions). The proposed metric is used to study the performance of typical nodes in both ad hoc and downlink cellular networks. The ad hoc network is modeled as a Poisson bipolar network with a fixed distance between each transmitter and its intended receiver. The cellular network is also modeled as a homogeneous Poisson point process. For both these setups, we use tools from stochastic geometry to derive the distribution of N-slot average rate in the following three cases: (i) rate across N time slots is completely correlated, (ii) rate across N time slots is independent and identically distributed, and (iii) rate across N time slots is partially correlated. While the reality is close to third case, the exact characterization of the first two extreme cases exposes certain important design insights. / Master of Science

京都大学 / 新制・課程博士 / 博士(理学) / 甲第25091号 / 理博第4998号 / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)教授 日野 正訓, 教授 COLLINSBenoit Vincent Pierre, 教授 楠岡 誠一郎 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

This thesis concerns measuring, understanding and modelling Internet traffic. We first study the origins of the statistical properties of Internet traffic, in particular its scaling behaviour, and propose a constructive model of packet traffic with physically motivated parameters. We base our analysis on a large amount of empirical data measured on different networks, and use a so called semi-experimental approach to isolate certain features of traffic we seek to model. These results lead to the choice of a particular Poisson cluster process, known as Bartlett-Lewis point process, for a new packet traffic model. This model has a small number of parameters with simple networking meaning, and is mathematically tractable. It allows us to gain valuable insight on the underlying mechanisms creating the observed statistics. / In practice, Internet traffic measurements are limited by the very large amount of data generated by high bandwidth links. This leads us to also investigate traffic sampling strategies and their respective inversion methods. We argue that the packet sampling mechanism currently implemented in Internet routers is not practical when one wants to infer the statistics of the full traffic from partial measurements. We advocate the use of flow sampling for many purposes. We show that such sampling strategy is much easier to invert and can give reasonable estimates of higher order traffic statistics such as distribution of number of packets per flow and spectral density of the packet arrival process. This inversion technique can also be used to fit the Bartlett-Lewis point process model from sampled traffic. / We complete our understanding of Internet traffic by focusing on the small scale behaviour of packet traffic. To do so, we use data from a fully instrumented Tier-1 router and measure the delays experienced by all the packets crossing it. We present a simple router model capable of simply reproducing the measured packet delays, and propose a scheme to export router performance information based on busy periods statistics. We conclude this thesis by showing how the Bartlett-Lewis point process can model the splitting and merging of packet streams in a router.

Fitting of parametric models to spatial and space-time point patterns has been a very active research area in the last few years. Concerning clustered patterns, the Cox point process is the model of choice. To avoid the computationally demanding maximum likelihood estimation or Bayesian inference, several estimation methods based on the moment properties of the processes in question were proposed in the literature. We give overview of the state-of-the-art moment estimation methods for stationary spatial Cox point processes and compare their performance in a simulation study. We also discuss generalization of such methods for inhomogeneous spatial point processes. In the core part of the thesis we focus on minimum contrast estimation for inhomogeneous space-time shot-noise Cox point processes and investigate the possibility to use projections to the spatial and temporal domain to estimate different parts of the model separately. We propose a step-wise estimation procedure based on projection processes and also a refined method which remedies the problem of possible cluster overlapping. We establish consistency and asymptotic normality of the estimators for both methods under the increasing window asymptotics and compare their performance on middle-sized observation windows by means of a simulation study....

The global effort to rehabilitate and restore destroyed mangrove forests is unable to keep up with the high mangrove deforestation rates which exceed the average pace of global deforestation by three to five times. Our knowledge of the underlying processes of mangrove forest regeneration is too limited in order to find suitable techniques for the restoration of degraded mangrove areas. The general objective of my dissertation was to improve mangrove restoration by understanding regeneration processes and local plant-plant interaction in a regenerating Avicennia germinans forest. The study was conducted in a high-shore mangrove forest area on the Ajuruteua peninsula, State of Para, Northern Brazil. The dwarf forest consisting of shrub-like trees is recovering from a stand-replacing event caused by a road construction in 1974 which interrupted the tidal inundation of the study area. Consequently, infrequent inundation and high porewater salinity limit tree growth and canopy closure. All trees and seedlings were stem-mapped in six 20 m x 20 m plots which were located along a tree density gradient. Moreover, height, crown extent, basal stem diameter of trees were measured. The area of herbaceous ground vegetation and wood debris were mapped as well. The mapped spatial distribution of trees, seedlings and covariates was studied using point pattern analysis and point process models, such as Gibbs and Thomas point process, in order to infer underlying ecological processes, such as seed dispersal, seedling establishment, tree recruitment and tree interaction. In the first study (chapter 2), I analyzed the influence of abiotic and biotic factors on the seedling establishment and tree recruitment of A. germinans during the recolonization of severely degraded mangrove sites using point process modeling. Most seedlings established adjacent to adult trees especially under their crown cover. Moreover, seedling density was higher within patches of the herbaceous salt-marsh plants Blutaparon portulacoides and Sesuvium portulacastrum than in uncovered areas. The higher density of recruited A. germinans trees in herb patches indicated that ground vegetation did not negatively influence tree development of A. germinans. In addition, tree recruitment occurred in clusters. Coarse wood debris had no apparent effect on either life stage. These results confirm that salt-marsh vegetation acts as the starting point for mangrove recolonization and indicate that the positive interaction among trees accelerates forest regeneration. In the second study (chapter 3), I analyzed how intraspecific interaction among A. germinans trees determines their growth and size under harsh environmental conditions. Interaction among a higher number of neighboring trees was positively related to the development of a focal tree. However, tree height, internode length and basal stem diameter were only positively associated in low-density forest stands (1.2 trees m-2) and not in forest stands of higher tree density (2.7 trees m-2). These results indicated a shift from facilitation, i.e. a positive effect of tree interaction, towards a balance between facilitation and competition. In the third study (chapter 4), I used point process modeling and the individual-based model mesoFON to disentangle the impact of regeneration and interaction processes on the spatial distribution of seedlings and trees. In this infrequently inundated area, propagules of A. germinans are only dispersed at a maximum distance of 3 m from their parent tree. Furthermore, there is no evidence that the following seedling establishment is influenced by trees. I was able to differentiate positive and negative tree interactions simulated by the mangrove model mesoFON regardless of dispersal processes based on static tree size information using the mark-correlation function. The results of this dissertation suggest that mangrove forest regeneration in degraded areas is a result of facilitative and not competitive interactions among mangrove trees, seedling and herbaceous vegetation. This has important implications for the restoration of degraded mangrove forest. Degraded mangrove areas are usually restored by planting a high number of evenly spaced seedlings. However, high costs constrain this approach to small areas. Assisting natural regeneration could be a less costly alternative. Herbaceous vegetation plays a crucial role in forest recolonization by entrapping propagules and possibly ameliorating harsh environmental conditions. So far only competition among mangrove trees has been considered during restoration. However, facilitative tree interactions could be utilized by planting seedling clusters in order to assist natural regeneration instead of planting seedlings evenly-spaced over large areas. This dissertation also showed that point pattern analysis and point process modeling can enable forest ecologists to describe the spatial distribution of trees as well as to infer underlying ecological processes.

Owing to its ability to improve both spectral and energy efficiency of wireless networks, massive multiple-input multiple-output (mMIMO) has become one of the key enablers of the fifth-generation (5G) and beyond communication systems. For successful integration of this promising physical layer technique in the upcoming cellular standards, it is essential to have a comprehensive understanding of its network-level performance. Over the last decade, stochastic geometry has been instrumental in obtaining useful system design insights of wireless networks through accurate and tractable theoretical analysis. Hence, it is only natural to consider modeling and analyzing the mMIMO systems using appropriate statistical constructs from the stochastic geometry literature and gain insights for its future implementation. With this broader objective in mind, we first focus on modeling a cellular mMIMO network that uses fractional pilot reuse to mitigate the sole performance-limiting factor of mMIMO networks, namely, pilot contamination. Leveraging constructs from the stochastic geometry literature, such as Johnson-Mehl cells, we derive analytical expressions for the uplink (UL) signal-to-interference-and-noise ratio (SINR) coverage probability and average spectral efficiency for a random user. From our system analysis, we present a partitioning rule for the number of pilot sequences to be reserved for the cell-center and cell-edge users that improves the average cell-edge user spectral efficiency while achieving similar cell-center user spectral efficiency with respect to unity pilot reuse. In addition, using the analytical approach developed for the cell-center user performance evaluation, we study the performance of a small cell system where user and base station (BS) locations are coupled. The impact of distance-dependent UL power control on the performance of an mMIMO network with unity pilot reuse is analyzed and subsequent system design guidelines are also presented. Next, we focus on the performance analysis of the cell-free mMIMO network, which is a distributed implementation of the mMIMO system that leads to the second and third contributions of this dissertation. Similar to the cellular counterpart, the cell-free systems also suffer from pilot contamination due to the reuse of pilot sequences throughout the network. Inspired by a hardcore point process known as the random sequential adsorption (RSA) process, we develop a new distributed pilot assignment algorithm that mitigates the effect of pilot contamination by ensuring a minimum distance among the co-pilot users. This pilot assignment scheme leads to the construction of a new point process, namely the multilayer RSA process. We study the statistical properties of this point process both in one and two-dimensional spaces by deriving approximate but accurate expressions for the density and pair correlation functions. Leveraging these new results, for a cell-free network with the proposed RSA-based pilot assignment scheme, we present an analytical approach that determines the minimum number of pilots required to schedule a user with probabilistic guarantees. In addition, to benchmark the performance of the RSA-based scheme, we propose two optimization-based centralized pilot allocation schemes using linear programming principles. Through extensive numerical simulations, we validate the efficacy of the distributed and scalable RSA-based pilot assignment scheme compared to the proposed centralized algorithms. Apart from pilot contamination, another impediment to the performance of a cell-free mMIMO is limited fronthaul capacity between the baseband unit and the access points (APs). In our fourth contribution, using appropriate stochastic geometry-based tools, we model and analyze the downlink of such a network for two different implementation scenarios. In the first scenario, we consider a finite network where each AP serves all the users in the network. In the second scenario, we consider an infinite network where each user is served by a few nearby APs in order to limit the load on fronthaul links. From our analyses, we observe that for the finite network, the achievable average system sum-rate is a strictly quasi-concave function of the number of users in the network, which serves as a key guideline for scheduler design for such systems. Further, for the user-centric architecture, we observe that there exists an optimal number of serving APs that maximizes the average user rate. The fifth and final contribution of this dissertation focuses on the potential improvement that is possible by the use of mMIMO in citizen broadband radio service (CBRS) spectrum sharing systems. As a first concrete step, we present comprehensive modeling and analysis of this system with omni-directional transmissions. Our model takes into account the key guidelines by the Federal Communications Commission for co-existence between licensed and unlicensed networks in the 3.5 GHz CBRS frequency band. Leveraging the properties of the Poisson hole process and Matern hardcore point process of type II, a.k.a. ghost RSA process, we analytically characterize the impact of different system parameters on various performance metrics such as medium access probability, coverage probability, and area spectral efficiency. Further, we provide useful system design guidelines for successful co-existence between these networks. Building upon this omni-directional model, we also characterize the performance benefits of using mMIMO in such a spectrum sharing network. / Doctor of Philosophy / The emergence of cloud-based video and audio streaming services, online gaming platforms, instantaneous sharing of multimedia contents (e.g., photos, videos) through social networking platforms, and virtual collaborative workspace/meetings require the cellular communication networks to provide high data-rate as well as reliable and ubiquitous connectivity. These constantly evolving requirements can be met by designing a wireless network that harmoniously exploits the symbiotic co-existence among different types of cutting-edge wireless technologies. One such technology is massive multiple-input multiple-output (mMIMO), whose core idea is to equip the cellular base stations (BSs) with a large number of antennas that can be leveraged through appropriate signal processing algorithms to simultaneously accommodate multiple users with reduced network interference. For successful deployment of mMIMO in the upcoming cellular standards, i.e., fifth-generation (5G) and beyond systems, it is necessary to characterize its performance in a large-scale wireless network taking into account the inherent spatial randomness in the BS and user locations. To achieve this goal, in this dissertation, we propose different statistical methods for the performance analysis of mMIMO networks using tools from stochastic geometry, which is a field of mathematics related to the study of random patterns of points. One of the major deployment issues of mMIMO systems is pilot contamination, which is a form of coherent network interference that degrades user performance. The main reason behind pilot contamination is the reuse of pilot sequences, which are a finite number of known signal waveforms used for channel estimation between a user and its serving BS. Further, the effect of pilot contamination is more severe for the cell-edge users, which are farther from their own BSs. An efficient scheme to mitigate the effect of pilot contamination is fractional pilot reuse (FPR). However, the efficiency of this scheme depends on the pilot partitioning rule that decides the fraction of total pilot sequences that should be used by the cell-edge users. Using appropriate statistical constructs from the stochastic geometry literature, such as Johnson-Mehl cells, we present a partitioning rule for efficient implementation of the FPR scheme in a cellular mMIMO network. Next, we focus on the performance analysis of the cell-free mMIMO network. In contrast to the cellular network, where each user is served by a single BS, in a cell-free network each user can be served by multiple access points (APs), which have less complex hardware compared to a BS. Owing to this cooperative and distributed implementation, there are no cell-edge users. Similar to the cellular counterpart, the cell-free systems also suffer from pilot contamination due to the reuse of pilot sequences throughout the network. Inspired by a hardcore point process known as the random sequential adsorption (RSA) process, we develop a new distributed pilot assignment algorithm that mitigates the effect of pilot contamination by ensuring a minimum distance among the co-pilot users. Further, we show that the performance of this distributed pilot assignment scheme is appreciable compared to different centralized pilot assignment schemes, which are algorithmically more complex and difficult to implement in a network. Moreover, this pilot assignment scheme leads to the construction of a new point process, namely the multilayer RSA process. We derive the statistical properties of this point process both in one and two-dimensional spaces. Further, in a cell-free mMIMO network, the APs are connected to a centralized baseband unit (BBU) that performs the bulk of the signal processing operations through finite capacity links, such as fiber optic cables. Apart from pilot contamination, another implementational issue associated with the cell-free mMIMO systems is the finite capacity of fronthaul links that results in user performance degradation. Using appropriate stochastic geometry-based tools, we model and analyze this network for two different implementation scenarios. In the first scenario, we consider a finite network where each AP serves all the users in the network. In the second scenario, we consider an infinite network where each user is served by a few nearby APs. As a consequence of this user-centric implementation, for each user, the BBU only needs to communicate with fewer APs thereby reducing information load on fronthaul links. From our analyses, we propose key guidelines for the deployment of both types of scenarios. The type of mMIMO systems that are discussed in this work will be operated in the sub-6 GHz frequency range of the electromagnetic spectrum. Owing to the limited availability of spectrum resources, usually, spectrum sharing is encouraged among different cellular operators in such bands. One such example is the citizen broadband radio service (CBRS) spectrum sharing systems proposed by the Federal Communications Commission (FCC). The final contribution of this dissertation focuses on the potential improvement that is possible by the use of mMIMO in the CBRS systems. As our first step, using tools from stochastic geometry, we model and analyze this system with a single antenna at the BSs. In our model, we take into account the key guidelines by the FCC for co-existence between licensed and unlicensed operators. Leveraging properties of the Poisson hole process and hardcore process, we provide useful theoretical expressions for different performance metrics such as medium access probability, coverage probability, and area spectral efficiency. These results are used to obtain system design guidelines for successful co-existence between these networks. We further highlight the potential improvement in the user performance with multiple antennas at the unlicensed BS.

Le changement climatique actuel est tellement rapide que la plupart des espèces ligneuses tempérées européennes telles que Fagus sylvatica risquent de ne pouvoir s'adapter, ni migrer suffisamment pour répondre à ce changement. La plupart des modèles simulant l'aire de répartition potentielle de la végétation en fonction du climat considèrent une dispersion « illimitée » ou « nulle » ce qui rend difficile l'évaluation de l'importance de la dispersion par rapport au climat dans la dynamique de la végétation. Ce travail de thèse a pour objectif d'intégrer à un modèle d'aire de répartition basé sur les processus (Phenofit) un modèle phénoménologique de dispersion (modèle de dispersion de Gibbs) dans le but de dissocier l'effet du climat de l'effet de la dispersion dans la réponse de Fagus sylvatica aux changements climatiques en Europe, (i) pendant la recolonisation postglaciaire de 12000 ans BP à l'actuel et (ii) pendant le 21ème siècle. Nos résultats montrent un fort impact de la dispersion associé à un effet également important de la localisation des refuges glaciaires sur la recolonisation postglaciaire du hêtre comparé à l'effet du climat de 12000 ans BP à l'actuel. En revanche, les capacités de dispersion du hêtre ne lui permettent pas d'occuper la totalité de son aire potentielle notamment au nord de l'Europe d'ici 2100. Cette faible colonisation vers le nord de l'Europe associée à de fortes extinctions au sud de son aire de répartition causées par l'augmentation du stress hydrique conduit à une diminution drastique de l'aire de répartition du hêtre d'ici la fin du 21ème siècle. / Current climate change is so fast that some temperate tree species, like Fagus sylvatica, could not adapt nor migrate fast enough to tract their climatic niche. Most models simulating the potential distribution of vegetation as a function of climate consider unlimited or "null" dispersal, which doesn't allow assessing the importance of dispersal compared to climate in the dynamics of the vegetation. In this thesis, we integrate into a process-based species distribution model (Phenofit), a phenomenological model of dispersal (Gibbs-based model) in order to disentangle the effects of climate and dispersal in the response of Fagus sylvatica to climate change in Europe, (i) during the postglacial recolonization from 12000 years BP to present, (ii) during the 21st century. Our results show strong impact of dispersal associated with a strong effect of glacial refugees location on the beech postglacial recolonization, compared to the effect of climat e since 12000 years. Nevertheless, beech dispersal abilities are not sufficient to allow the colonization of newly suitable areas in northern Europe by 2100. This low colonization rate in Northern Europe in addition to a high extinction rate in Southern Europe due to increasing drought lead to a drastic reduction of beech distribution by the end of the 21st century.

Ce manuscrit est dédié à l'étude de l'estimation paramétrique d'une famille de processus ponctuels appelée processus déterminantaux. Ces processus sont utilisés afin de générer et modéliser des configurations de points possédant de la dépendance négative, dans le sens où les points ont tendance à se repousser entre eux. Plus précisément, nous étudions les propriétés asymptotiques de divers estimateurs classiques de processus déterminantaux paramétriques, stationnaires et non-stationnaires, dans les cas où l'on observe une unique réalisation d'un tel processus sur une fenêtre bornée. Ici, l'asymptotique se fait sur la taille de la fenêtre et donc, indirectement, sur le nombre de points observés. Dans une première partie, nous montrons un théorème limite central pour une classe générale de statistiques sur les processus déterminantaux. Dans une seconde partie, nous montrons une inégalité de béta-mélange générale pour les processus ponctuels que nous appliquons ensuite aux processus déterminantaux. Dans une troisième partie, nous appliquons le théorème limite central obtenu à la première partie à une classe générale de fonctions estimantes basées sur des méthodes de moments. Finalement, dans la dernière partie, nous étudions le comportement asymptotique du maximum de vraisemblance des processus déterminantaux. Nous donnons une approximation asymptotique de la log-vraisemblance qui est calculable numériquement et nous étudions la consistance de son maximum. / This manuscript is devoted to the study of parametric estimation of a point process family called determinantal point processes. These point processes are used to generate and model point patterns with negative dependency, meaning that the points tend to repel each other. More precisely, we study the asymptotic properties of various classical parametric estimators of determinantal point processes, stationary and non stationary, when considering that we observe a unique realization of such a point process on a bounded window. In this case, the asymptotic is done on the size of the window and therefore, indirectly, on the number of observed points. In the first chapter, we prove a central limit theorem for a wide class of statistics on determinantal point processes. In the second chapter, we show a general beta-mixing inequality for point processes and apply our result to the determinantal case. In the third chapter, we apply the central limit theorem showed in the first chapter to a wide class of moment-based estimating functions. Finally, in the last chapter, we study the asymptotic behaviour of the maximum likelihood estimator of determinantal point processes. We give an asymptotic approximation of the log-likelihood that is computationally tractable and we study the consistency of its maximum.

Dans une première partie, j'étudie un processus de stockage de données en temps continu où le disque dur est identifié à la droite réelle. Ce modèle est une version continu du problème original de Parking de Knuth. Ici l'arrivée des fichiers est Poissonienne et le fichier se stocke dans les premiers espaces libres à droite de son point d'arrivée, quitte à se fragmenter. Dans un premier temps, je construis le modèle et donne une caractérisation géométrique et analytique de la partie du disque recouverte au temps t. Ensuite j'étudie les régimes asymptotiques au moment de saturation du disque. Enfin, je décris l'évolution en temps d'un block de données typique. La deuxième partie est constituée de l'étude de processus de branchement, motivée par des questions d'infection cellulaire. Dans un premier temps, je considère un processus de branchement en environnement aléatoire sous-critique, et détermine les théorèmes limites en fonction de la population initiale, ainsi que des propriétes sur les environnements, les limites de Yaglom et le Q-processus. Ensuite, j'utilise ce processus pour établir des résultats sur un modèle décrivant la prolifération d'un parasite dans une cellule en division. Je détermine la probabilité de guérison, le nombre asymptotique de cellules inféctées ainsi que les proportions asymptotiques de cellules infectées par un nombre donné de parasites. Ces différents résulats dépendent du régime du processus de branchement en environnement aléatoire. Enfin, j'ajoute une contamination aléatoire par des parasites extérieures.