We consider one-dimensional excited random walks (ERWs) with iid Markovian cookie
stacks in the non-boundary recurrent regime. We prove that under diffusive scaling such an …

We use generalized Ray–Knight theorems, introduced by B. Tóth in 1996, together with
techniques developed for excited random walks as main tools for establishing positive and …

We show convergence of a family of one-dimensional self-interacting random walks to
Brownian motion perturbed at extrema under the diffusive scaling. This completes the …

We prove a quenched invariance principle for a class of random walks in random
environment on Z d, where the walker alters its own environment. The environment consists …

We consider excited random walk (ERW) on $\mathbb {Z} $ in environments with identical
stacks of infinitely many cookies at each site, subject to the constraint that the total drift per …

ONE-DIMENSIONAL EXCITED RANDOM WALK WITH UNBOUNDEDLY MANY EXCITATIONS
PER SITE Page 1 ONE-DIMENSIONAL EXCITED RANDOM WALK WITH UNBOUNDEDLY …

In this thesis we study two unary stochastic abelian networks: random walk with local
memory, and branching processes in a Markovian environment. The first part is joint work …

Ce document présente la majorité de mes travaux de recherche réalisés depuis mon
doctorat. Ces travaux sont classés selon quatre chapitres, le regroupement étant thématique …