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Transactions of the American Mathematical Society

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

 

 

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
MathSciNet review: 0326867
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Abstract: Let $ p(x,y)$ be the transition function for a symmetric, irreducible, transient Markov chain on the countable set S. Let $ {\eta _t}$ 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 $ {\eta _t}$ in terms of the bounded functions on S which are harmonic with respect to $ p(x,y)$. Ergodic theorems are proved concerning the convergence of the system to an invariant measure.


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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