This paper studies the mixing behavior of the Asymmetric Simple Exclusion Process (ASEP)
on a segment of length N. Our main result is that for particle densities in (0, 1), the total …

We study the speed of convergence to equilibrium for the asymmetric simple exclusion
process (ASEP) on a finite interval with one open boundary. We provide sharp estimates on …

This article generalizes the small noise cutoff phenomenon obtained recently by Barrera,
Högele and Pardo (JSP2021) to the mild solutions of the stochastic heat equation and the …

We consider a natural analogue of Brownian motion on free orthogonal quantum groups
and prove that it exhibits a cutoff at time N ln (N). Then, we study the induced classical …

We consider the Metropolis biased card shuffling (also called the multi-species ASEP on a
finite interval or the random Metropolis scan). Its convergence to stationarity was believed to …

In this paper, we study an ordinary differential equation with a degenerate global attractor at
the origin, to which we add a white noise with a small parameter that regulates its intensity …

We prove that the limit profile of star transpositions at time $ t= n\log n+ cn $ is equal to $ d_
{\text {TV}}(\text {Poiss}(1+ e^{-c}),\text {Poiss}(1)) $. We prove this by developing a …

We study mixing times of the one-sided $ k $-transposition shuffle. We prove that this shuffle
mixes relatively slowly, even for $ k $ big. Using the recent" lifting eigenvectors" technique of …

The purpose of this paper is to provide a complete description of the eigenvalues of the
generator of a neutral multi-type Moran model, and the applications to the study of the speed …

We introduce a technique for comparing the limit profile behavior of two reversible,
commuting Markov chains on the same space, that share the same stationary distribution …