Local limit approximations for Lagrangian distributions.
Local limit theorems for non-identical integer valued random variables, to appear theory probability. Applications
Localization and delocalization for heavy tailed band matrices
We consider some random band matrices with band-width whose entries are independent random variables with distribution tail in . We consider the largest eigenvalues and the associated eigenvectors and prove the following phase transition. On the one hand, when , the largest eigenvalues have order , are asymptotically distributed as a Poisson process and their associated eigenvectors are essentially carried by two coordinates (this phenomenon has already been remarked for full matrices by Soshnikov...
Loi multidimensionnelle de Cauchy comme une distribution limite des sommes de vecteurs aléatoires dépendants
Loop-free Markov chains as determinantal point processes
We show that any loop-free Markov chain on a discrete space can be viewed as a determinantal point process. As an application, we prove central limit theorems for the number of particles in a window for renewal processes and Markov renewal processes with Bernoulli noise.