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Markov chains, R-trivial monoids and representation theory

Ayyer, Arvind and Schilling, Anne and Steinberg, Benjamin and Thiery, Nicolas M (2015) Markov chains, R-trivial monoids and representation theory. In: INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, 25 (1-2). pp. 169-231.

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Official URL: http://dx.doi.org/10.1142/S0218196715400081

Abstract

We develop a general theory of Markov chains realizable as random walks on R-trivial monoids. It provides explicit and simple formulas for the eigenvalues of the transition matrix, for multiplicities of the eigenvalues via Mobius inversion along a lattice, a condition for diagonalizability of the transition matrix and some techniques for bounding the mixing time. In addition, we discuss several examples, such as Toom-Tsetlin models, an exchange walk for finite Coxeter groups, as well as examples previously studied by the authors, such as nonabelian sandpile models and the promotion Markov chain on posets. Many of these examples can be viewed as random walks on quotients of free tree monoids, a new class of monoids whose combinatorics we develop.

Item Type: Journal Article
Additional Information: Copy right for this article belongs to the WORLD SCIENTIFIC PUBL CO PTE LTD, 5 TOH TUCK LINK, SINGAPORE 596224, SINGAPORE
Keywords: Markov chains; R-trivial monoids; representation theory
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Depositing User: Id for Latest eprints
Date Deposited: 29 Apr 2015 04:54
Last Modified: 29 Apr 2015 04:54
URI: http://eprints.iisc.ac.in/id/eprint/51448

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