Markov chains, $\mathscr R$-trivial monoids and representation theory
In: Ayyer, Arvind; Schilling, Anne; Steinberg, Benjamin; & Thiery, Nicolas M.(2014). Markov chains, $\mathscr R$-trivial monoids and representation theory. International Journal of Algebra and Computation, Volume 25, Issue 01n02, 169 (2015). doi: 10.1142/S0218196715400081. UC Davis: Department of Mathematics. Retrieved from: http://www.escholarship.org/uc/item/350622bt International Journal of Algebra and Computation (IJAC) International Journal of Algebra and Computation (IJAC), 2015, pp.1540008. ⟨10.1142/s0218196715400081⟩; (2014-01-17)
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Zugriff:
We develop a general theory of Markov chains realizable as random walks on $\mathscr R$-trivial monoids. It provides explicit and simple formulas for the eigenvalues of the transition matrix, for multiplicities of the eigenvalues via M\"obius 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.
Comment: Dedicated to Stuart Margolis on the occasion of his sixtieth birthday; 71 pages; final version to appear in IJAC
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Markov chains, $\mathscr R$-trivial monoids and representation theory
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| Autor/in / Beteiligte Person: | Steinberg, Benjamin ; Thiéry, Nicolas M. ; Ayyer, Arvind ; Schilling, Anne ; Indian Institute of Science Education and Research Thiruvananthapuram (IISER TVM) ; Department of Mathematics [Davis] ; University of California [Davis] (UC Davis) ; University of California-University of California ; City College of New York [CUNY] (CCNY) ; City University of New York [New York] (CUNY) ; Graphes, Algorithmes et Combinatoire (LRI) (GALaC - LRI) ; Laboratoire de Recherche en Informatique (LRI) ; Université Paris-Sud - Paris 11 (UP11)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS) |
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| Quelle: | Ayyer, Arvind; Schilling, Anne; Steinberg, Benjamin; & Thiery, Nicolas M.(2014). Markov chains, $\mathscr R$-trivial monoids and representation theory. International Journal of Algebra and Computation, Volume 25, Issue 01n02, 169 (2015). doi: 10.1142/S0218196715400081. UC Davis: Department of Mathematics. Retrieved from: http://www.escholarship.org/uc/item/350622bt International Journal of Algebra and Computation (IJAC) International Journal of Algebra and Computation (IJAC), 2015, pp.1540008. ⟨10.1142/s0218196715400081⟩; (2014-01-17) |
| Veröffentlichung: | eScholarship, University of California, 2014 |
| Medientyp: | unknown |
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