A characterization of the invariant measures for an infinite particle system with interactions
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- by Thomas M. Liggett PDF
- Trans. Amer. Math. Soc. 179 (1973), 433-453 Request permission
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.References
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Additional Information
- © Copyright 1973 American Mathematical Society
- 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