Large deviations upper bounds and central limit theorems for non-commutative functionals of gaussian large random matrices

Abstract. In this paper, motivated by some applications in branching random walks, we improve and extend his theorems in the sense that: 1) we prove that the central limit theorem

Chapter 3 is devoted to establishing limit theorems for products of random matrices which will be used in the following chapters for the study of a branching random walk with

We revisit Wschebor’s theorems on small increments for processes with scaling and stationary properties and deduce large deviation principles.. Keywords: Brownian motion,

We establish a large deviation principle for the empirical spec- tral measure of a sample covariance matrix with sub-Gaussian entries, which extends Bordenave and Caputo’s result

chains., Ann. Nagaev, Some limit theorems for stationary Markov chains, Teor. Veretennikov, On the Poisson equation and diffusion approximation. Rebolledo, Central limit theorem

On a fait l’état de l’art de la protection qui existe au niveau du réseau de distribution électrique moyenne tension HTA (utilisé aussi par la société

Dans le second chapitre, on s’attachera à obtenir des inégalités de concentration qui reflètent le comportement de grandes déviations de diverses fonctionnelles spec- trales, comme

P´ech´e [Pe] pointed out a sharp phase transition phenomenon : according to the largest eigenvalue of the perturbation, the largest eigenvalue of the perturbed matrix should