arXiv subjects

Brune Massoulié

Publications and source records attributed to Brune Massoulié.

4 recordsLinked to original sources

arXiv2026

Cutoff for the mixing time of the Facilitated Exclusion Process

We compute the mixing time of the Facilitated Exclusion Process (FEP) and obtain cutoff and pre-cutoff in different regimes. The main tool to obtain this result is a new bijective, deterministic mapping between the joint law of an ergodic FEP and its current through the origin, and the joint law of a Symmetric Simple Exclusion Process (SSEP) and its current through the origin. This mapping is interesting in itself, as it remains valid in the non-ergodic regime where it gives a coupling between the position of a tagged particle in the FEP and the current through the origin in a SSEP with traps.

math.PR↗

arXiv2025

Velocity trapping in the lifted TASEP and the true self-avoiding random walk

We discuss non-reversible Markov-chain Monte Carlo algorithms that, for particle systems, rigorously sample the positional Boltzmann distribution and that have faster than physical dynamics. These algorithms all feature a non-thermal velocity distribution. They are exemplified by the lifted TASEP (totally asymmetric simple exclusion process), a one-dimensional lattice reduction of event-chain Monte Carlo. We analyze its dynamics in terms of a velocity trapping that arises from correlations between the local density and the particle velocities. This allows us to formulate a conjecture for its out-of-equilibrium mixing time scale, and to rationalize its equilibrium superdiffusive time scale. Both scales are faster than for the (unlifted) TASEP. They are further justified by our analysis of the lifted TASEP in terms of many-particle realizations of true self-avoiding random walks. We discuss velocity trapping beyond the case of one-dimensional lattice models and in more than one physical dimensions. Possible applications beyond physics are pointed out.

cond-mat.stat-mech↗

arXiv2024

Cutoff for the transience and mixing time of a SSEP with traps and consequences on the FEP

We introduce a new particle system that we call the SSEP with traps, which is non reversible, attractive, and has a transient regime. We study its \emph{transience time} $θ_K$, meaning the time after which the system is no longer in a transient state with high probability, on the ring with $K$ sites. We first show that $θ_K$ is of order $K^2 \log K$ for a system of size $K$, and more precisely that it exhibits a cutoff at time $\frac{1}{π^2} K^2 \log K$. We then show that its \emph{mixing time} also undergoes cutoff at the same time. We further define a new mapping between the SSEP with traps and the Facilitated Exclusion Process (FEP) which has attracted significant scrutiny in recent years. We expect that this mapping will be a very useful tool to study the FEP's microscopic and macroscopic behaviour. In particular, using this mapping, we show that the FEP's transience time also undergoes a cutoff at time $\frac{1}{4 π^2} N^2 \log N$. Notably, our results show that for a FEP with particle density strictly greater than $\frac12$, the transient component is exited in a diffusive time. This allows to extend the upper-bound from [Ayre Chleboun 2024] for the mixing time of the FEP with particle density $ρ> 1/2$.

math.PR↗

arXiv2023

Wetting on a wall and wetting in a well: Overview of equilibrium properties

We study the wetting model, which considers a random walk constrained to remain above a hard wall, but with additional pinning potential for each contact with the wall. This model is known to exhibit a wetting phase transition, from a localized phase (with trajectories pinned to the wall) to a delocalized phase (with unpinned trajectories). As a preamble, we take the opportunity to present an overview of the model, collecting and complementing well-known and other folklore results. Then, we investigate a version with elevated boundary conditions, which has been studied in various contexts both in the physics and the mathematics literature; it can alternatively be seen as a wetting model in a square well. We complement here existing results, focusing on the equilibrium properties of the model, for a general underlying random walk (in the domain of attraction of a stable law). First, we compute the free energy and give some properties of the phase diagram; interestingly, we find that, in addition to the wetting transition, a so-called saturation phase transition may occur. Then, in the so-called Cramér's region, we find an exact asymptotic equivalent of the partition function, together with a (local) central limit theorem for the fluctuations of the left-most and right-most pinned points, jointly with the number of contacts at the bottom of the well.

math.PR↗