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14 Markov Chains

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Representation Theory of Finite Monoids

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Abstract

A Markov chain is a stochastic process on a finite state space such that the system evolves from one state to another according to a prescribed probabilistic law. For example, card shuffling can be modeled via a Markov chain. The state space is all 52! orderings of a deck of cards. Each step of the Markov chain corresponds to performing a riffle shuffle to the deck.

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Notes

  1. 1.

    In probability theory, it is traditional to use the transpose of what we are calling the transition matrix. However, because we are using left actions and left modules, it is more natural for us to use this formulation.

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Authors and Affiliations

  1. Department of Mathematics, The City College of New York (CCNY), New York, NY, USA

    Benjamin Steinberg

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  1. Benjamin Steinberg
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Steinberg, B. (2016). 14 Markov Chains. In: Representation Theory of Finite Monoids. Universitext. Springer, Cham. https://doi.org/10.1007/978-3-319-43932-7_14

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