Related papers: Mixing time of a matrix random walk generated by e…

We consider a flip dynamics for directed (1+d)-dimensional lattice paths with length L. The model can be interpreted as a higher dimensional version of the simple exclusion process, the latter corresponding to the case d=1. We prove that…

A 1-2 model configuration is a subset of edges of a hexagonal lattice satisfying the constraint that each vertex is incident to 1 or 2 edges. We introduce Markov chains to sample the 1-2 model configurations on 2D hexagonal lattice and…

We consider continuous-time Markov chain on a finite state space X. We assume X can be clustered into several subsets such that the intra-transition rates within these subsets are of order $\mathcal{O}(\frac{1}{\epsilon})$ comparing to the…

We show that the modified log-Sobolev constant for a natural Markov chain which converges to an $r$-homogeneous strongly log-concave distribution is at least $1/r$. Applications include a sharp mixing time bound for the bases-exchange walk…

We use coupling to study the time taken until the distribution of a statistic on a Markov chain is close to its stationary distribution. Coupling is a common technique used to obtain upper bounds on mixing times of Markov chains, and we…

The problem of efficiently sampling from a set of(undirected) graphs with a given degree sequence has many applications. One approach to this problem uses a simple Markov chain, which we call the switch chain, to perform the sampling. The…

We show a strict hierarchy among various edge and vertex expansion properties of Markov chains. This gives easy proofs of a range of bounds, both classical and new, on chi-square distance, spectral gap and mixing time. The 2-gradient is…

We prove a Chernoff-type bound for sums of matrix-valued random variables sampled via a regular (aperiodic and irreducible) finite Markov chain. Specially, consider a random walk on a regular Markov chain and a Hermitian matrix-valued…

We develop a method for analyzing the mixing times for a quite general class of Markov chains on the complete monomial group G \wr S_n (the wreath product of a group G with the permutation group S_n) and a quite general class of Markov…

Recently Wilson [Ann. Appl. Probab. 14 (2004) 274--325] introduced an important new technique for lower bounding the mixing time of a Markov chain. In this paper we extend Wilson's technique to find lower bounds of the correct order for…

Consider the random walk on the $n \times n$ upper triangular matrices with ones on the diagonal and elements over $\mathbb{F}_p$ where we pick a row at random and either add it or subtract it from the row directly above it. The main result…

We extend a technique for lower-bounding the mixing time of card-shuffling Markov chains, and use it to bound the mixing time of the Rudvalis Markov chain, as well as two variants considered by Diaconis and Saloff-Coste. We show that in…

In Diaconis and Saloff-Coste (1996), the authors introduced the simple ``transvection" walk on $\mathrm{GL}_n(\mathbb F_2)$: at each step, choose two distinct rows and add one to the other. In Ben-Hamou (2025), the author recently proved…

The problem of sampling from the stationary distribution of a Markov chain finds widespread applications in a variety of fields. The time required for a Markov chain to converge to its stationary distribution is known as the classical…

The convergence rate of a Markov chain to its stationary distribution is typically assessed using the concept of total variation mixing time. However, this worst-case measure often yields pessimistic estimates and is challenging to infer…

We give a bound on the mixing time of a uniformly ergodic, reversible Markov chain in terms of the spectral radius of the transition operator. This bound has been established previously in finite state spaces, and is widely believed to hold…

Let $X$ be a finite set and let $G$ be a finite group acting on $X$. The group action splits $X$ into disjoint orbits. The Burnside process is a Markov chain on $X$ which has a uniform stationary distribution when the chain is lumped to…

In this paper, we investigate the properties of a random walk on the alternating group $A_n$ generated by $3$-cycles of the form $(i,n-1,n)$ and $(i,n,n-1)$. We call this the transpose top-$2$ with random shuffle. We find the spectrum of…

We provide new upper bounds for mixing times of general finite Markov chains. We use these bounds to show that the total variation mixing time is robust under rough isometry for bounded degree graphs that are roughly isometric to trees.

The theory of rapid mixing random walks plays a fundamental role in the study of modern randomised algorithms. Usually, the mixing time is measured with respect to the worst initial position. It is well known that the presence of…