Related papers: Limit profiles and cutoff for the Burnside process…

We consider Markov decision processes with synchronizing objectives, which require that a probability mass of $1-\epsilon$ accumulates in a designated set of target states, either once, always, infinitely often, or always from some point…

We study mixing times for the totally asymmetric simple exclusion process (TASEP) on a circle of length $N$ with $k$ particles. We show that the mixing time is of order $N^2 \min(k,N-k)^{-1/2}$, and that the cutoff phenomenon does not…

We investigate the mixing time of the capacity $k$ simple exclusion process (also called the partial exclusion process) of Schultz and Sandow with $m$ particles on a segment of length $N$. We show that the $k$-SEP exhibits cutoff at time…

This paper gives a necessary and sufficient condition for a sequence of birth and death chains to converge abruptly to stationarity, that is, to present a cut-off. The condition involves the notions of spectral gap and mixing time. Y. Peres…

The random transposition shuffle on repeated cards induces a Markov chain on the quotient space of arrangements with multiplicities, and is equivalent to the many-urn mean-field Bernoulli-Laplace model introduced by Scarabotti. Writing…

Let $G$ be a finite group. The commuting chain on $G$ moves from an element $x$ to $y$ by selecting $y$ uniformly amongst those which commute with $x$. The $t$ step transition probabilities of this chain converge to a distribution uniform…

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…

Let $P_n$ be a Sylow $p$-subgroup of the symmetric group $S_n$. We investigate the number and sizes of the $P_n\setminus S_n\ /\ P_n$ double cosets, showing that most double cosets have maximal size when $p$ is odd, or equivalently, that…

Consider a sequence of continuous-time irreducible reversible Markov chains and a sequence of initial distributions, $\mu_n$. The sequence is said to exhibit $\mu_n$-cutoff if the convergence to stationarity in total variation distance is…

Families of symmetric simple random walks on Cayley graphs of Abelian groups with a bound on the number of generators are shown to never have sharp cut off in the sense of [1], [3], or [5]. Here convergence to the stationary distribution is…

Consider an N-dimensional Markov chain obtained from N one-dimensional random walks by Doob h-transform with the q-Vandermonde determinant. We prove that as N becomes large, these Markov chains converge to an infinite-dimensional Feller…

Consideration is given to the three different analytical methods for the computation of upper bounds for the rate of convergence to the limiting regime of one specific class of (in)homogeneous continuous-time Markov chains. This class is…

We consider Markov decision processes (MDP) as generators of sequences of probability distributions over states. A probability distribution is p-synchronizing if the probability mass is at least p in a single state, or in a given set of…

We study the convergence to equilibrium of the Dyson-Jacobi process, a system of n interacting particles on the segment [0, 1] arising from Random Matrix Theory. We establish the occurence of a cutoff phenomenon for the intrinsic…

We study the asymmetric simple exclusion process (ASEP) on a segment $\{1,\ldots,b_N\}$ and are interested in its total variation distance to equilibrium when started from an initial configuration $\xi^{N}$. We provide a general result…

We investigate the convergence in distribution of sequential empirical processes of dependent data indexed by a class of functions F. Our technique is suitable for processes that satisfy a multiple mixing condition on a space of functions…

Given a sequence $(\mathfrak{X}_i, \mathscr{K}_i)_{i=1}^\infty$ of Markov chains, the cut-off phenomenon describes a period of transition to stationarity which is asymptotically lower order than the mixing time. We study mixing times and…

We investigate the mixing properties of a model of reversible Markov chains in random environment, which notably contains the simple random walk on the superposition of a deterministic graph and a second graph whose vertex set has been…

This paper gives new, efficient algorithms for approximate uniform sampling of contingency tables and integer partitions. The algorithms use the Burnside process, a general algorithm for sampling a uniform orbit of a finite group acting on…

It has been recently suggested that a totally asymmetric exclusion process with two species on an open chain could exhibit spontaneous symmetry breaking in some range of the parameters defining its dynamics. The symmetry breaking is…