Related papers: Mixing Time for Some Adjacent Transposition Markov…
We prove an upper bound on the total variation mixing time of a finite Markov chain in terms of the absolute spectral gap and the number of elements in the state space. Unlike results requiring reversibility or irreducibility, this bound is…
This paper studies Markov chains on the symmetric group $S_n$ where the transition probabilities are given by the Ewens distribution with parameter $\theta>1$. The eigenvalues are identified to be proportional to the content polynomials of…
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…
The standard coalescent is widely used in evolutionary biology and population genetics to model the ancestral history of a sample of molecular sequences as a rooted and ranked binary tree. In this paper, we present a representation of the…
Let $P$ be a bistochastic matrix of size $n$, and let $\Pi$ be a permutation matrix of size $n$. In this paper, we are interested in the mixing time of the Markov chain whose transition matrix is given by $Q=P\Pi$. In other words, the chain…
We analyze the mixing time of a natural local Markov chain (the Glauber dynamics) on configurations of the solid-on-solid model of statistical physics. This model has been proposed, among other things, as an idealization of the behavior of…
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…
The approximate uniform sampling of graph realizations with a given degree sequence is an everyday task in several social science, computer science, engineering etc. projects. One approach is using Markov chains. The best available current…
We study the convergence rate to stationarity for a class of exchangeable partition-valued Markov chains called cut-and-paste chains. The law governing the transitions of a cut-and-paste chain are determined by products of i.i.d. stochastic…
In this paper, we propose a new Markov chain which generalizes random-to-random shuffling on permutations to random-to-random shuffling on linear extensions of a finite poset of size $n$. We conjecture that the second largest eigenvalue of…
In a series of recent works, Boyd, Diaconis, and their co-authors have introduced a semidefinite programming approach for computing the fastest mixing Markov chain on a graph of allowed transitions, given a target stationary distribution.…
By viewing the $N$-simplex as the set of positions of $N-1$ ordered particles on the unit interval, the adjacent walk is the continuous time Markov chain obtained by updating independently at rate 1 the position of each particle with a…
We consider a Markov chain on invertible $n\times n$ matrices with entries in $\mathbb{Z}_2$ which moves by picking an ordered pair of distinct rows and add the first one to the other, modulo $2$. We establish a logarithmic Sobolev…
A joint degree matrix (JDM) specifies the number of connections between nodes of given degrees in a graph, for all degree pairs and uniquely determines the degree sequence of the graph. We consider the space of all balanced realizations of…
In this paper we consider a simple Markov chain for bipartite graphs with given degree sequence on $n$ vertices. We show that the mixing time of this Markov chain is bounded above by a polynomial in $n$ in case of {\em semi-regular} degree…
Many finite-state reversible Markov chains can be naturally decomposed into "projection" and "restriction" chains. In this paper we provide bounds on the total variation mixing times of the original chain in terms of the mixing properties…
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…
We provide a general framework for computing upper bounds on mixing times of finite Markov chains when its minimal ideal is left zero. Our analysis is based on combining results by Brown and Diaconis with our previous work on stationary…
In this paper we consider the problem of sampling from the low-temperature exponential random graph model (ERGM). The usual approach is via Markov chain Monte Carlo, but Bhamidi et al. showed that any local Markov chain suffers from an…
Markov chain Monte Carlo (MCMC) algorithms are ubiquitous in probability theory in general and in machine learning in particular. A Markov chain is devised so that its stationary distribution is some probability distribution of interest.…