Nicolas Bouchot

activity

20222025

collaborators

6 papers

math.PR2025

Covering of an inner subset by the confined random walk

Nicolas Bouchot

We consider the simple random walk conditioned to stay forever in a finite domain $D_{N} \subset Z^{d}, d \geq 3$ of typical size $N$ . This confined walk is a random walk on t…

math.PR2025

How thin does random interlacement have to be so that a random walk can see through it?

Nicolas Bouchot

The random interlacements $I (u)$ at level $u$ has been introduced by Sznitman, as a Poissonian collection of independent simple random walk trajectories on $Z^{d}$ …

math.PR2024

Some properties of the principal Dirichlet eigenfunction in Lipschitz domains, via probabilistic couplings

Quentin Berger, Nicolas Bouchot

We study a discrete and continuous version of the spectral Dirichlet problem in an open bounded connected set $Ω \subset R^{d}$ , in dimension $d \geq 2$ . More precisely, consi…

math.PR2024

A confined random walk locally looks like tilted random interlacements

Nicolas Bouchot

In this paper we consider the simple random walk on $Z^{d}$ , $d \geq 3$ , conditioned to stay in a large domain $D_{N}$ of typical diameter $N$ . Considering the range up to tim…

math.PR2023

Scaling limit of a one-dimensional polymer in a repulsive i.i.d. environment

Nicolas Bouchot

The purpose of this paper is to study a one-dimensional polymer penalized by its range and placed in a random environment $ω$ . The law of the simple symmetric random walk up to tim…

math.PR2022

Scaling limits for the random walk penalized by its range in dimension one

Nicolas Bouchot

In this article we study a one dimensional model for a polymer in a poor solvent: the random walk on $Z$ penalized by its range. More precisely, we consider a Gibbs transf…