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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Existence theorems for infinite particle systems


Author: Thomas M. Liggett
Journal: Trans. Amer. Math. Soc. 165 (1972), 471-481
MSC: Primary 60K35
DOI: https://doi.org/10.1090/S0002-9947-1972-0309218-7
MathSciNet review: 0309218
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Abstract: Sufficient conditions are given for a countable sum of bounded generators of semigroups of contractions on a Banach space to be a generator. This result is then applied to obtain existence theorems for two classes of models of infinite particle systems. The first is a model of a dynamic lattice gas, while the second describes a lattice spin system.


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DOI: https://doi.org/10.1090/S0002-9947-1972-0309218-7
Keywords: Infinite particle systems, linear semigroups of contractions, statistical mechanics
Article copyright: © Copyright 1972 American Mathematical Society