Ergodic theorems for graph interactions
- 1 March 1975
- journal article
- research article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 7 (01), 179-194
- https://doi.org/10.1017/s0001867800040350
Abstract
A criterion for ergodicity of lattice interactions has been given by Dobrushin [2], and improved by Harris [3] and Holley [5]. In this paper we present a simplified derivation of these results, and obtain stronger conditions for interactions on the one- and two-dimensional integer lattices, and the 3–Bethe lattice.Keywords
This publication has 2 references indexed in Scilit:
- An ergodic theorem for interacting systems with attractive interactionsProbability Theory and Related Fields, 1972
- Existence theorems for infinite particle systemsTransactions of the American Mathematical Society, 1972