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Exclusion Processes

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Book cover Stochastic Interacting Systems: Contact, Voter and Exclusion Processes

Part of the book series: Grundlehren der mathematischen Wissenschaften ((GL,volume 324))

Abstract

A common feature of the contact processes and voter models that are treated in Parts I and II is that only one coordinate of the configuration changes at each time. One consequence of this property is that these processes tend to have only a few invariant measures — typically there are one or two trivial ones, and then with a substantial amount of work, one can often prove the existence of a nontrivial invariant measure. The reason for this scarcity of invariant measures is that the process has no conserved quantity, i.e., a quantity that does not change with time. The existence of a conserved quantity tends to break up the state space {0, 1}S into classes determined by the value of this quantity, and then there tends to be an invariant measure for each of its possible values. This corresponds roughly to the difference between irreducible and reducible Markov chains.

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  1. Mathematics Department, University of California, Los Angeles, CA, 90095-1555, USA

    Thomas M. Liggett

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© 1999 Springer-Verlag Berlin Heidelberg

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Liggett, T.M. (1999). Exclusion Processes. In: Stochastic Interacting Systems: Contact, Voter and Exclusion Processes. Grundlehren der mathematischen Wissenschaften, vol 324. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03990-8_4

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  • DOI: https://doi.org/10.1007/978-3-662-03990-8_4

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