Related papers: Making Markov chains less lazy

In this study, a new extension of the Markov Renewal theory is introduced by allowing time to evolve in multiple dimensions. The resulting chains are referred to as multi-time Markov Renewal chains and since this extension is new, the state…

We construct strong stationary dual chains for Ising model on a circle, non-symmetric random walk on square lattice and a random walk on hypercube. The strong stationary dual chains are all sharp and have the same state space as original…

In the Fastest Mixing Markov Chain problem, we are given a graph $G = (V, E)$ and desire the discrete-time Markov chain with smallest mixing time $\tau$ subject to having equilibrium distribution uniform on $V$ and non-zero transition…

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…

The cover time of a Markov chain on a finite state space is the expected time until all states are visited. We show that if the cover time of a discrete-time Markov chain with rational transitions probabilities is bounded, then it is a…

Let $P$ be the transition matrix of a finite, irreducible and reversible Markov chain. We say the continuous time Markov chain $X$ has transition matrix $P$ and speed $\lambda$ if it jumps at rate $\lambda$ according to the matrix $P$. Fix…

We consider continuous-space, discrete-time Markov chains on $\mathbb{R}^d$, that admit a finite number $N$ of metastable states. Our main motivation for investigating these processes is to analyse random Poincar\'e maps, which describe…

We prove an $\widetilde O(n^2)$ bound for the relaxation time and the log-Sobolev time (inverse log-Sobolev constant) of the classical triangulation flip chain on a convex $(n+2)$-gon, implying a mixing time of $\widetilde O(n^2)$. The…

Using elementary methods, we prove that for a countable Markov chain $P$ of ergodic degree $d > 0$ the rate of convergence towards the stationary distribution is subgeometric of order $n^{-d}$, provided the initial distribution satisfies…

About two dozens of exactly solvable Markov chains on one-dimensional finite and semi-infinite integer lattices are constructed in terms of convolutions of orthogonality measures of the Krawtchouk, Hahn, Meixner, Charlier, $q$-Hahn,…

We present a simple randomized procedure for the prediction of a binary sequence. The algorithm uses ideas from recent developments of the theory of the prediction of individual sequences. We show that if the sequence is a realization of a…

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…

General characterizations of ergodic Markov chains have been developed in considerable detail. In this paper, we study the transience for discrete-time Markov chains on general state spaces, including the geometric transience and algebraic…

We develop a general theory of Markov chains realizable as random walks on $\mathscr R$-trivial monoids. It provides explicit and simple formulas for the eigenvalues of the transition matrix, for multiplicities of the eigenvalues via…

This paper aims at improving the convergence to equilibrium of finite ergodic Markov chains via permutations and projections. First, we prove that a specific mixture of permuted Markov chains arises naturally as a projection under the KL…

We study a large class of reversible Markov chains with discrete state space and transition matrix $P_N$. We define the notion of a set of {\it metastable points} as a subset of the state space $\G_N$ such that (i) this set is reached from…

We introduce a framework for obtaining tight mixing times for Markov chains based on what we call restricted modified log-Sobolev inequalities. Modified log-Sobolev inequalities (MLSI) quantify the rate of relative entropy contraction for…

We consider symmetric Markov chains on $\Bbb Z^d$ where we do {\bf not} assume that the conductance between two points must be zero if the points are far apart. Under a uniform second moment condition on the conductances, we obtain upper…

A finite ergodic Markov chain is said to exhibit cutoff if its distance to stationarity remains close to 1 over a certain number of iterations and then abruptly drops to near 0 on a much shorter time scale. Discovered in the context of card…

We establish the existence and uniqueness of quasi-stationary and quasi-ergodic measures for almost surely absorbed discrete-time Markov chains under weak conditions. We obtain our results by exploiting Banach lattice properties of…