A characterization of the invariant measures for an infinite particle system with interactions

Author:
Thomas M. Liggett

Journal:
Trans. Amer. Math. Soc. **179** (1973), 433-453

MSC:
Primary 60K35

DOI:
https://doi.org/10.1090/S0002-9947-1973-0326867-1

MathSciNet review:
0326867

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be the transition function for a symmetric, irreducible, transient Markov chain on the countable set *S*. Let be the infinite particle system on *S* with the simple exclusion interaction and one-particle motion determined by *p*. A characterization is obtained of all the invariant measures for in terms of the bounded functions on *S* which are harmonic with respect to . Ergodic theorems are proved concerning the convergence of the system to an invariant measure.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1973-0326867-1

Keywords:
Infinite particle systems,
invariant measures,
ergodic theorems

Article copyright:
© Copyright 1973
American Mathematical Society