Remote Access Transactions of the American Mathematical Society
Green Open Access

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. II


Author: Thomas M. Liggett
Journal: Trans. Amer. Math. Soc. 198 (1974), 201-213
MSC: Primary 60K35
DOI: https://doi.org/10.1090/S0002-9947-1974-0375531-2
MathSciNet review: 0375531
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ p(x,y)$ be the transition function for a symmetric, irreducible 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$. The present author and Spitzer have determined all of the invariant measures of $ \eta (t)$, and have obtained ergodic theorems for $ \eta (t)$, under two different sets of assumptions. In this paper, these problems are solved in the remaining case.


References [Enhancements On Off] (What's this?)

  • [1] R. Holley, A class of interactions in an infinite particle system, Advances in Math. 5 (1970), 291-309. MR 42 #3857. MR 0268960 (42:3857)
  • [2] J. Kemeny, J. Snell, and A. Knapp, Denumerable Markov chains, Van Nostrand, Princeton, N. J., 1966. MR 34 #6858. MR 0207042 (34:6858)
  • [3] T. Liggett, A characterization of the invariant measures for an infinite particle system with interactions, Trans. Amer. Math. Soc. 179 (1973), 433-453. MR 0326867 (48:5209)
  • [4] -, Existence theorems for infinite particle systems, Trans. Amer. Math. Soc. 165 (1972), 471-481. MR 0309218 (46:8328)
  • [5] F. Spitzer, Interaction of Markov processes, Advances in Math. 5 (1970), 246-290. MR 42 #3856. MR 0268959 (42:3856)
  • [6] -, Recurrent random walk of an infinite particle system, Trans. Amer. Math. Soc. 198 (1974), 191-199. MR 0375533 (51:11724)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 60K35

Retrieve articles in all journals with MSC: 60K35


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1974-0375531-2
Keywords: Infinite particle systems, invariant measures, ergodic theorems
Article copyright: © Copyright 1974 American Mathematical Society

American Mathematical Society