Related papers: Countable Markov shifts with exponential mixing

Cover time, in the context of dynamical systems, quantifies the rate at which orbits cover the system. We prove that for countable full shifts with a Gibbs measure, equipped with a natural metric, the rate of covering of orbits of points…

Consider a Markov process \omega_t at equilibrium and some event C (a subset of the state-space of the process). A natural measure of correlations in the process is the pairwise correlation \Pr[\omega_0,\omega_t \in C] - \Pr[\omega_0 \in…

We deal with countable alphabet locally compact random subshifts of finite type (the latter merely meaning that the symbol space is generated by an incidence matrix) under the absence of Big Images Property and under the absence of uniform…

Strong typicality and the Markov lemma have been used in the proofs of several multiterminal source coding theorems. Since these two tools can be applied to finite alphabets only, the results proved by them are subject to the same…

Starting from a Markov chain with a finite alphabet, we consider the chain obtained when all but one symbol are undistinguishable for the practitioner. We study necessary and sufficient conditions for this chain to have continuous…

Chaotic dynamics with sensitive dependence on initial conditions may result in exponential decay of correlation functions. We show that for one-dimensional interval maps the corresponding quantities, that is, Lyapunov exponents and…

This work is a continuation of [Kalikaeva, MPRF, 23(2):225-240]. The object of study is ``Markov-up processes'' on $\mathbb Z_+$ and the moment of downcrossing a certain barrier. The processes considered in this paper differ from Markov…

We discuss how the simultaneous crossovers of deconfinement and chiral restoration can be realized. We propose a dynamical mechanism assuming that the effective potential gives a finite value of the chiral condensate if the Polyakov loop…

A wide class of ``counting'' problems have been studied in Computer Science. Three typical examples are the estimation of - (i) the permanent of an $n\times n$ 0-1 matrix, (ii) the partition function of certain $n-$ particle Statistical…

The notion of a successful coupling of Markov processes, based on the idea that both components of the coupled system ``intersect'' in finite time with probability one, is extended to cover situations when the coupling is unnecessarily…

We consider a time-homogeneous Markov chain $X_n$, $n\ge0$, valued in ${\bf R}$. Suppose that this chain is transient, that is, $X_n$ generates a $\sigma$-finite renewal measure. We prove the key renewal theorem under condition that this…

We study hyperbolic attractors of some dynamical systems with apriori given countable Markov partitions. Assuming that contraction is stronger than expansion we construct new Markov rectangles such that their crossections by unstable…

We prove that the limit profile of a sequence of reversible Markov chains exhibiting total variation cutoff is a continuous function, under a computable condition involving the spectrum of the transition matrix and the cutoff window.

In this work we obtain mixing (and in some cases sharp mixing rates) for a reasonable large class of invertible systems preserving an infinite measure. The examples considered here are the invertible analogue of both Markov and non Markov…

We introduce a correlation number for two strictly positive, locally H\"older continuous, independent potentials with strong entropy gaps at infinity on a topologically mixing countable state Markov shift with BIP. We define in this way a…

The influence of a time-periodic forcing on stochastic processes can essentially be emphasized in the large time behaviour of their paths. The statistics of transition in a simple Markov chain model permits to quantify this influence. In…

This review paper provides an introduction of Markov chains and their convergence rates which is an important and interesting mathematical topic which also has important applications for very widely used Markov chain Monte Carlo (MCMC)…

Let $\Om$ be a Borel subset of $S^\Bbb N$ where $S$ is countable. A measure is called exchangeable on $\Om$, if it is supported on $\Om$ and is invariant under every Borel automorphism of $\Om$ which permutes at most finitely many…

It is shown that for a non-singular conservative shift on a topologically mixing Markov subshift with Doeblin Condition the only possible absolutely continuous shift-invariant measure is a Markov measure. Moreover, if it is not equivalent…

For full shifts on finite alphabets, Coelho and Quas showed that the map that sends a H\"older continuous potential $\phi$ to its equilibrium state $\mu_\phi$ is $\overline{d}$-continuous. We extend this result to the setting of full shifts…