Fast mixing for the low temperature 2d Ising model through irreversible parallel dynamics
Probability
2014-07-25 v1
Abstract
We study metastability and mixing time for a non-reversible probabilistic cellular automaton. With a suitable choice of the parameters, we first show that the stationary distribution is close in total variation to a low temperature Ising model. Then we prove that both the mixing time and the time to exit a metastable state grow polynomially in the size of the system, while this growth is exponential in reversible dynamics. In this model, non-reversibility, parallel updatings and a suitable choice of boundary conditions combine to produce an efficient dynamical stability.
Cite
@article{arxiv.1407.6650,
title = {Fast mixing for the low temperature 2d Ising model through irreversible parallel dynamics},
author = {Paolo Dai Pra and Benedetto Scoppola and Elisabetta Scoppola},
journal= {arXiv preprint arXiv:1407.6650},
year = {2014}
}