Phase transition and correlation decay in Coupled Map Lattices

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.

References in corpus (2)

• Multicomponent dynamical systems: SRB measures and phase transitions
• Phase transitions in a piecewise expanding coupled map lattice with linear nearest neighbour coupling

Cited by in corpus (4)

• A Monte Carlo investigation of the critical behavior of Stavskaya's probabilistic cellular automaton
• Phase transitions in probabilistic cellular automata
• Exponential Decay of Correlations for Strongly Coupled Toom Probabilistic Cellular Automata
• Stability of the uniqueness regime for ferromagnetic Glauber dynamics under non-equilibrium perturbations