This thesis reports on a comprehensive experimental study of the collective dynamics of colloidal hard sphere suspensions. The main quantity measured is the coherent Intermediate Scattering Function (ISF) using a range of techniques based on Dynamic Light Scattering (DLS). The collective dynamics are measured as a function of scattering vector for volume fractions spanning from dilute samples, through the fluid phase and the metastable region, up until deep in the glass region. This work describes two major explorations: (i) the effect of volume of fraction on the q-dependency of the collective dynamics; and (ii) a study of the ageing processes in colloidal glasses. The present work is unique in the application of several advanced experimental techniques, and in the level of averaging that has been carried out, enabling a more sophisticated analysis than has previously been possible. This includes the characterization of non-Fickian processes and the determinatio n of the current-current correlation function (CCCF) in the metastable fluid, and the quantitative characterization of the ageing process in the hard sphere glass. In addition, by combining aspects of the coherent and incoherent ISFs, this work also allows the expression of the collective dynamics in terms of the single particle displacement. The results show a dynamical change at the freezing point (f), which exposes the incapacity of the system to dissipate thermal energy via diffusing momentum currents, i.e. viscous flow. The structural impediments responsible for this, associated with dynamical heterogeneities, begin at the structure factor peak, and spread to other spatial modes as the volume fraction increases. Above the glass transition (g), structural relaxation becomes arrested at all spatial modes probed, i.e. flow is arrested. It is found that, following the quench, samples above the glass volume fraction approach some final

Cette thèse présente des résultats nouveaux dans deux sujets de la physique statistique du désordre: les modèles aux energies aléatoires logarithmiquement corrélées (logREMs), et la transition de localisation dans les matrices aléatoires à longues portées.Dans la première partie consacrée aux logREMs, nous montrons comment décrire leurs points communs et les données spécifiques aux modèles particuliers. Ensuite nous appliquons la méthode de la brisure de symétrie des répliques pour les étudier en general, et en déduirons la transition vitreuse et le processus des minima, en termes de processus de Poisson décorés. Nous présentons également une série d'application des polynômes de Jack à la prédiction exactes des observables dans le modèle circulaire et ses variants. Finalement, nous décrivons les progrès récents sur la connexion exacte entre les logREMs et la théorie conforme de Liouville.La seconde partie a pour but d'introduire une nouvelle classe de matrices aléatoires à bandes, dite la classe des distributions larges; elle ressemble essentiellement aux matrices creuses. Nous étudions d'abord un modèle particulier de la classe, les matrices aléatoires Bêta, qui sont inspirées par une correspondence exacte à un modèle statistique récemment étudié, celui de la dynamique épidémique. A l'aide des arguments analytiques appuyés sur la correspondence et des simulations numériques, nous montrons l'existence des transitions de localisation avec des valeurs propres critiques dans le régime des paramètres dit d'exponentielle étirée. Ensuite, en utilisant une approche de renormalisation et de diagonalisation par blocs, nous soutenons que les transitions de localisation sont en général présentes dans la class des distributions larges. / This thesis presents original results in two domains of disordered statistical physics: logarithmic correlated Random Energy Models (logREMs), and localization transition in long-range random matrices.In the first part devoted to logREMs, we show how to characterise their common properties and model--specific data. Then we develop their replica symmetry breaking treatment, which leads to the freezing scenario of their free energy distribution and the general description of their minima process, in terms of decorated Poisson point process. We also report a series of new applications of the Jack polynomials in the exact predictions of some observables in the circular model and its variants. Finally, we present the recent progress on the exact connection between logREMs and the Liouville conformal field theory.The goal of the second part is to introduce and study a new class of banded random matrices, the broadly distributed class, which is characterid an effective sparseness. We will first study a specific model of the class, the Beta Banded random matrices, inspired by an exact mapping to a recently studied statistical model of long--range first--passage percolation/epidemics dynamics. Using analytical arguments based on the mapping and numerics, we show the existence of localisation transitions with mobility edges in the ``stretch--exponential'' parameter--regime of the statistical models. Then, using a block--diagonalization renormalization approach, we argue that such localization transitions occur generically in the broadly distributed class.