1306.6104 (Cesar Maldonado et al.)

Markov Approximations of Gibbs measures for long-range potentials on 1D
lattices    [PDF]

Cesar Maldonado, Raul Salgado-Garcia

We study one-dimensional lattice systems with pair-wise interactions of in?nite range. We show projective convergence of Markov measures to the unique equilibrium state. For this purpose we impose a slightly stronger condition than summability of variations on the regularity of the interaction. With our condition we are able to explicitly obtain stretched exponential bounds for the rate of mixing of the equilibrium state. Finally we show convergence for the entropy of the Markov measures to that of the equilibrium state via the convergence of their topological pressure.

View original: http://arxiv.org/abs/1306.6104