Relaxation of Product Markov Chains on Product Spaces

Relaxation of Product Markov Chains on Product Spaces

The purpose of the paper is studying the relaxation time of product{ type Markov chains on product spaces which approach a product distribution. We determine bounds to approach stationarity for such Markov chains in terms of the mixing times of the component Markov chains. In cases where the component mixing times vary much we propose an optimized visiting scheme which makes such product{type M...

On Product Connection Theorems for Markov Chains

This paper addresses the problem of constructing multidimensional Markov chains with product form steady state distribution. Product connection theorems are established which guarantee that the product ∏ ν π (ν) nν of steady state probabilities π (ν) nν related to ergodic Markov chains X (ν) = {X(ν)(t) : t ∈ T} represents the steady state probability p(n) = p(n1, n2, . . .) of an ergodic multid...

Designing product ciphers using Markov Chains

In this paper we consider the design of product ciphers based on Markov chains. We examine two particular chains which are related to the diierential and linear cryptanalysis attacks. Both of these chains approach the uniform distribution which indicates that appropriately designed ciphers are secure against these attacks. The maximum deviation from the uniform distribution can be used as guide...

Parabolic Marcinkiewicz integrals on product spaces

‎In this paper‎, ‎we study the $L^p$ ($1

Concentration inequalities on product spaces with applications to Markov processes