论文信息 - Ergodic theorems for graph interactions

Ergodic theorems for graph interactions

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.

D. Griffeath

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[2] T. E. Harris. Contact Interactions on a Lattice , 1974 .

[3] R. Holley. An ergodic theorem for interacting systems with attractive interactions , 1972 .

[4] T. Liggett. Existence theorems for infinite particle systems , 1972 .

[5] J. Marsden,et al. Lectures on analysis , 1969 .