Related papers: On a class of one-sided Markov shifts
Let $A$ be an $N\times N$ irreducible matrix with entries in $\{0,1\}$. We present an easy way to find an $(N+3)\times (N+3)$ irreducible matrix $\bar{A}$ with entries in $\{0,1\}$ such that their Cuntz--Krieger algebras ${\mathcal{O}}_A$…
We introduce and study a new model that we call the {\em matching model}. Items arrive one by one in a buffer and depart from it as soon as possible but by pairs. The items of a departing pair are said to be {\em matched}. There is a finite…
Product-form stationary distributions in Markov chains have been a foundational advance and driving force in our understanding of stochastic systems. In this paper, we introduce a new product-form relationship that we call "graph-based…
We consider general Markov chains with discrete time in an arbitrary measurable (phase) space and homogeneous in time. Markov chains are defined by the classical transition function which within the framework of the operator treatment…
For strongly positively recurrent countable state Markov shifts, we bound the distance between an invariant measure and the measure of maximal entropy in terms of the difference of their entropies. This extends an earlier result for…
A problem from thermodynamic formalism for countable symbolic Markov chains is considered. It concerns asymptotic behavior of the equilibrium measures corresponding to increasing sequences of finite sub-matrices of an infinite nonnegative…
The upper extremes of a Markov chain with regulary varying stationary marginal distribution are known to exhibit under general conditions a multiplicative random walk structure called the tail chain. More generally, if the Markov chain is…
This article studies the convergence properties of trans-dimensional MCMC algorithms when the total number of models is finite. It is shown that, for reversible and some non-reversible trans-dimensional Markov chains, under mild conditions,…
In the simple case of a Bernoulli shift on two symbols, zero and one, by permuting the symbols, it is obvious that any two equal entropy shifts are isomorphic. We show that the isomorphism can be realized by a factor that maps a binary…
We present here two standalone results from a forthcoming work on the analysis of Markov chains using the representation theory of $S_n$. First, we give explicit formulas for the decompositions of tensor powers of the defining and standard…
A new object of the probability theory, two-sided chain of events (symbols), is introduced. A theory of multi-steps Markov chains with long-range memory, proposed earlier in Phys. Rev. E 68, 06117 (2003), is developed and used to establish…
This paper is a didactic comment (a transcription with variations) to the paper of S.R. Foguel {\it Finite Dimensional Perturbations in Banach Spaces}. Addressed, mainly: postgraduates and related readers. Subject: Suppose we have two…
We obtain a complete classification of the continuous unitary representations of oligomorphic permutation groups (those include the infinite permutation group $S_\infty$, the automorphism group of the countable dense linear order, the…
Itzkowitz's problem asks whether every topological group $G$ has equal left and right uniform structures provided that bounded left uniformly continuous real-valued function on $G$ are right uniformly continuous. This paper provides a…
We prove an ergodic theorem for Markov chains indexed by the Ulam-Harris-Neveu tree over large subsets with arbitrary shape under two assumptions: with high probability, two vertices in the large subset are far from each other and have…
We consider for two based graphs $G$ and $H$ the sequence of graphs $G_k$ given by the wedge sum of $G$ and $k$ copies of $H$. These graphs have an action of the symmetric group $\Sigma_k$ by permuting the $H$-summands. We show that the…
We study the graphs formed from instances of the stable matching problem by connecting pairs of elements with an edge when there exists a stable matching in which they are matched. Our results include the NP-completeness of recognizing…
We introduce and study a unital version of shift equivalence for finite square matrices over the nonnegative integers. In contrast to the classical case, we show that unital shift equivalence does not coincide with one-sided eventual…
The first aim of this paper is to introduce a class of Markov chains on $\mathbb{Z}_+$ which are discrete self-similar in the sense that their semigroups satisfy an invariance property expressed in terms of a discrete random dilation…
In the paper, we study a new rate of convergence estimate for homogeneous discrete-time nonlinear Markov chains based on the Markov-Dobrushin condition. This result generalizes the convergence estimates for any positive number of transition…