Central Limit Theorems for Linear Statistics of Heavy Tailed Random Matrices

Actually, the limit analysis of the autocorrelation and distributions of the M -DWPT coefficients is more intricate than presented in [1] and [3] because, as shown below, this

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

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 prove that, in this case, the Open Quantum Random Walk behaves like a mixture of Open Quantum Random Walks with single Gaussian, that is, up to conditioning the trajectories at

Roughly speaking functional central limit theorems hold true as soon as the self-intersection local time of the random walk converges almost surely to some constant.. To be com-

Spectral theory; Objective method; Operator convergence; Logarithmic potential; Ran- dom matrices; Random Graphs; Heavy tailed distributions; α-stable

The proof is based on a new central limit theorem for dependent sequences with values in smooth Banach spaces, which is given in Section 3.1.1.. In Section 2.2, we state the

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