# Chains with Complete Connections: General Theory, Uniqueness, Loss of Memory and Mixing Properties

@article{Fernndez2003ChainsWC,
title={Chains with Complete Connections: General Theory, Uniqueness, Loss of Memory and Mixing Properties},
author={Roberto Fern{\'a}ndez and Gr'egory Maillard},
journal={Journal of Statistical Physics},
year={2003},
volume={118},
pages={555-588}
}
• Published 1 May 2003
• Mathematics
• Journal of Statistical Physics
We introduce a statistical mechanical formalism for the study of discrete-time stochastic processes with which we prove: (i) General properties of extremal chains, including triviality on the tail σ-algebra, short-range correlations, realization via infinite-volume limits and ergodicity. (ii) Two new sufficient conditions for the uniqueness of the consistent chain. The first one is a transcription of a criterion due to Georgii for one-dimensional Gibbs measures, and the second one corresponds…
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