Neste trabalho apresentamos condições suficientes para a obtenção de taxas exponenciais de convergência na lei multidimensional dos grandes números para campos aleatórios definidos em R^Z_d. Dentre possíveis aplicações do resultado apresentamos medidas não-gibbsianas e não-FKG (limites de saturaçãoo de processos de estacionamento) e medidas estacionárias originárias de sistemas de partículas (rede com perdas, incluindo o caso onde há interação de longo alcance com cauda pesada). / We describe sufficient conditions for the occurrence of exponential rates of convergence in the multidimensional law of large numbers for random fields in RZd . Non-gibbsian and non-FKG measures from statistical mechanics (jamming limits of RSA models) and IPS (stationary measures of loss networks, including heavy-tail long-range interaction) are indicated as examples where the result applies.

<p>In this thesis we present a model of the interacting agents on the financial market. The agents are represented by a non-Euclidean random graph, where each agent communicate with another with probability p, and the interaction according to the Ising Model. We investigate properties of the model by direct calculations for small graph sizes, and by perfect simulation for larger graph sizes. We also present a model for asset price variation by using the magnetization of the Ising model.</p>

Demand uncertainty has been recognized as one factor that may cause price dispersion in perfectly competitive markets with costly and perishable capacity. With the persistence of the degree of price dispersion in increasingly competitive markets, demand uncertainty has become more important for us to understand the phenomenon of fare inequality. This dissertation consists of three related studies on this topic. In the first study, Prescott (1975) model is extends by incorporating the heterogeneity of customers' reservation values. The model shows that the equilibrium price dispersion also depends on the mix of customers and their reservation values. With customer segmentation based on reservation values, the equilibrium price dispersion is more efficient than what can be achieved without segmentation. In the airline industry context, the model implies that different prices can exist simultaneously in the market and carriers would provide more seats if they can segment their travelers. This sheds light on an alternative motivation for airlines to require Saturday night stay over other than the practice of price discrimination. In the second study, a price simulation in the airline industry is conducted. The stochastic demand for coach class, nonstop, air travel service on the observed routs is calculated. Then a market price schedule based on Prescott's model is simulated by using nonparametric method. The comparison between the simulated price distribution and the actual price distribution provides evidence that on average more than 60 percent of the fare inequality on the observed routes can be accounted for by cost variation due to demand uncertainty under the condition of perfect competition. At last, an empirical model is specified to explore the relationship between route demand uncertainty and carrier price dispersion in U.S. air travel markets. The results demonstrate that the effect of route demand uncertainty on carrier price dispersion varies with the market structure. In monopoly market, the route demand uncertainty has no effect on carrier price dispersion. While in duopoly and competitive markets, the increase of route demand uncertainty is associated with the decrease of the carrier price dispersion. Furthermore, the negative relationship is magnified when the market becomes more competitive.

Perfect codes and minimal distance of a code have great importance in the study of theoryof codes. The perfect codes are classified generally and in particular for the Lee metric.However, there are very few perfect codes in the Lee metric. The Lee metric hasnice properties because of its definition over the ring of integers residue modulo q. It isconjectured that there are no perfect codes in this metric for q &gt; 3, where q is a primenumber.The minimal distance comes into play when it comes to detection and correction oferror patterns in a code. A few bounds on the number of codewords and minimal distanceof a code are discussed. Some examples for the codes are constructed and their minimaldistance is calculated. The bounds are illustrated with the help of the results obtained.

We consider complete subgraphs of the graph induced by the noncommutativity of a ring, and prove that the graph induced by an infinite noncommutative prime ring contains an infinite complete subgraph. We also compute the clique number and the chromatic number of the graphs induced by some concrete graphs.

This paper focuses on the issue of sampling directly from the stationary distribution of Vervaat perpetuities. It improves upon an algorithm for perfect sampling first presented by Fill & Huber by implementing both a faster multigamma coupler and a moving value of Xmax to increase the chance of unification. For beta = 1 we are able to reduce the expected steps for a sample by 22%, and at just beta = 3 we lower the expected time by over 80%. These improvements allow us to sample in reasonable time from perpetuities with much higher values of beta than was previously possible.

Partially Recursive Acceptance Rejection (PRAR) and bounding chains used in conjunction with coupling from the past (CFTP) are two perfect simulation protocols which can be used to sample from a variety of unnormalized target distributions. This paper first examines and then implements these two protocols to sample from the hardcore gas process. We empirically determine the subset of the hardcore process's parameters for which these two algorithms run in polynomial time. Comparing the efficiency of these two algorithms, we find that PRAR runs much faster for small values of the hardcore process's parameter whereas the bounding chain approach is vastly superior for large values of the process's parameter.

Partially Recursive Acceptance Rejection (PRAR) and bounding chains used in conjunction with coupling from the past (CFTP) are two perfect simulation protocols which can be used to sample from a variety of unnormalized target distributions. This paper first examines and then implements these two protocols to sample from the hardcore gas process. We empirically determine the subset of the hardcore process's parameters for which these two algorithms run in polynomial time. Comparing the efficiency of these two algorithms, we find that PRAR runs much faster for small values of the hardcore process's parameter whereas the bounding chain approach is vastly superior for large values of the process's parameter.

The study of coding theory aims to detect and correct the errors during the transmission of the data. It enhances the quality of data transmission and provides better control over the noisy channels.The perfect codes are collected and analyzed in the premises of the Hamming metric.This classification yields that there exists only a few perfect codes. The perfect codes do not guarantee the perfection by all means but just satisfy certain bound and properties. The detection and correction of errors is always very important for better data transmission.

Let <b>A</b> and <b>B</b> be finite sets with |<b>A</b>|=<i>n</i> and |<b>B</b>|=<i>m</i>. An (<i>n</i>,<i>m</i>,<i>w</i>)-<i>perfect hash</i> family</i> is a collection <i>F</i> of functions from <b>A</b> to <b>B</b> such that for any <b>X</b> &#8838; <b>A</b> with |<b>X</b>|=<i>w</i>, there exists at least one ? &#8712; <i>F</i> such that ? is one-to-one when restricted to <b>X</b>. Perfect hash families are basic combinatorial structures and they have played important roles in Computer Science in areas such as database management, operating systems, and compiler constructions. Such hash families are used for memory efficient storage and fast retrieval of items such as reserved words in programming languages, command names in interactive systems, or commonly used words in natural languages. More recently, perfect hash families have found numerous applications to cryptography, for example, to broadcast encryption schemes, secret sharing, key distribution patterns, visual cryptography, cover-free families and secure frameproof codes. In this thesis, we survey constructions and applications of perfect hash families. For constructions, we divided the results into three parts, depending on underlying structure and properties of the constructions: combinatorial structures, linear functionals, and algebraic structures. For applications, we focus on those related to cryptography.