Crested products of Markov chains

Simple item page
dc.creatorD'Angeli, Daniele
dc.creatorDonno, Alfredo
dc.date2009-03-03
dc.date.accessioned2026-07-07T12:48:40Z
dc.date.available2026-07-07T12:48:40Z
dc.descriptionIn 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.
dc.descriptionPublished in at http://dx.doi.org/10.1214/08-AAP546 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/0903.0513
dc.identifierhttp://arxiv.org/abs/0903.0513
dc.identifierAnnals of Applied Probability 2009, Vol. 19, No. 1, 414-453
dc.identifierdoi:10.1214/08-AAP546
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/222134
dc.subjectProbability
dc.subject60J10, 15A69, 05E30, 05C25, 43A85 (Primary)
dc.titleCrested products of Markov chains
dc.typetext

Files

Collections

arXiv