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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Additional Information

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