Crested products of Markov chains

D'Angeli, Daniele; Donno, Alfredo

doi:10.1214/08-AAP546

Scientific article

English

Crested products of Markov chains

Contributors

D'Angeli, Daniele; Donno, Alfredo

Published in

The Annals of applied probability, vol. 19, no. 1, p. 414-453

Publication date

2009

Abstract

In this work we define two kinds of crested product for reversible Markov chains, which naturally appear as a generalization of the case of crossed and nested product, as in association schemes theory, even if we do a construction that seems to be more general and simple. Although the crossed and nested product are inspired by the study of Gelfand pairs associated with the direct and the wreath product of two groups, the crested products are a more general construction, independent from the Gelfand pairs theory, for which a complete spectral theory is developed. Moreover, the k-step transition probability is given. It is remarkable that these Markov chains describe some classical models (Ehrenfest diffusion model, Bernoulli–Laplace diffusion model, exclusion model) and give some generalization of them. As a particular case of nested product, one gets the classical Insect Markov chain on the ultrametric space. Finally, in the context of the second crested product, we present a generalization of this Markov chain to the case of many insects and give the corresponding spectral decomposition.

UNIGE affiliation entities

Faculté des sciences / Section de mathématiques

Citation (ISO format)

D’ANGELI, Daniele, DONNO, Alfredo. Crested products of Markov chains. In: The Annals of applied probability, 2009, vol. 19, n° 1, p. 414–453. doi: 10.1214/08-AAP546

Article (Accepted version)

Identifiers

PID : unige:8517
DOI : 10.1214/08-AAP546
arXiv : 0903.0513v1

Additional URL for this publication

http://projecteuclid.org/euclid.aoap/1235140344

Journal ISSN

1050-5164

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01/07/2010 15:27:00

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Crested products of Markov chains

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Published in

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Abstract

UNIGE affiliation entities

Citation (ISO format)

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