Phase transition and correlation decay in Coupled Map Lattices

Details Phase transition and correlation decay in Coupled Map Lattices Phase transition and correlation decay in Coupled Map Lattices

2009-06-17

arxiv.org/abs/0906.3017v2

Communications in Mathematical Physics: Volume 297, Issue 1 (2010), Page 229.

Mathematics

Dynamical Systems

Scientific paper

10.1007/s00220-010-1041-8

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.

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