Eigenvectors for a random walk on a left-regular band
type: Item
instance of: scholarly article
title: Eigenvectors for a random walk on a left-regular band
zbMATH Open document ID: 1252.60008
published in: Advances in Applied Mathematics
publication date: 2012-03-29T00:00:00Z
review text: Random walks on left regular bands were first introduced and analyzed by \textit{K. S. Brown} [J. Theor. Probab. 13, No. 3, 871--938 (2000; Zbl 0980.60014)]. A special type of left regular bands are the semigroup of faces of a hyperplane arrangement. In this article, the author presents a simple construction of eigenvectors for the transition matrices of random walks on left regular bands. This is achieved by a decomposition of the transitional matrices into a linear combinations of orthogonal idempotents by specializing a simple recursive method introduced by the author [Int. J. Algebra Comput. 17, No. 8, 1593--1610 (2007; Zbl 1148.16024)].This method provides a simpler alternative prove to some known results on random walks on left regular bands. The author also explain at the end of the paper how to use the poset topology to extract an eigenbasis for the transition matrices of the hyperplane chamber walks.
reviewed by: Norbert Youmbi
Mathematics Subject Classification ID: 60B15
Mathematics Subject Classification ID: 52C35
zbMATH DE Number: 6019327
zbMATH Keywords: random walk
zbMATH Keywords: Markov chain
zbMATH Keywords: semigroup
zbMATH Keywords: hyperplane arrangement
author: Franco Saliola
MaRDI profile type: Publication
full work available at URL: j.aam.2011.09.002
OpenAlex ID: W2051669952
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cites work: Facing up to arrangements: face-count formulas for partitions of space by hyperplanes
DOI: 10.1016/J.AAM.2011.09.002
description: scientific article; zbMATH DE number 6019327