Phase transition and correlation decay in Coupled Map Lattices
Dynamical Systems
2010-05-19 v2 Mathematical Physics
math.MP
Abstract
For a Coupled Map Lattice with a specific strong coupling emulating Stavskaya's probabilistic cellular automata, we prove the existence of a phase transition using a Peierls argument, and exponential convergence to the invariant measures for a wide class of initial states using a technique of decoupling originally developed for weak coupling. This implies the exponential decay, in space and in time, of the correlation functions of the invariant measures.
Cite
@article{arxiv.0906.3017,
title = {Phase transition and correlation decay in Coupled Map Lattices},
author = {Augustin de Maere},
journal= {arXiv preprint arXiv:0906.3017},
year = {2010}
}