Phase transition and correlation decay in Coupled Map Lattices

TL;DR

This paper proves the existence of a phase transition and exponential decay of correlations in a specific coupled map lattice model, using novel techniques for strong coupling scenarios.

Contribution

It introduces a new approach to establish phase transitions and correlation decay in coupled map lattices with strong coupling, extending previous weak coupling methods.

Findings

Existence of a phase transition in the model

Exponential convergence to invariant measures

Correlation functions decay exponentially in space and time

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.