Basic Ideas to Approach Metastability in Probabilistic Cellular Automata

TL;DR

This paper reviews the metastable behavior of Probabilistic Cellular Automata, highlighting challenges and unique features compared to traditional statistical mechanics models, and discusses approaches to understanding their complex dynamics.

Contribution

It provides a comprehensive overview of metastability in Probabilistic Cellular Automata, emphasizing the difficulties and peculiarities in analyzing their metastable states.

Findings

Identifies key challenges in analyzing metastability in Probabilistic Cellular Automata

Highlights differences between Probabilistic Cellular Automata and standard lattice models

Discusses methodological approaches to studying metastable behavior

Abstract

Cellular Automata are discrete--time dynamical systems on a spatially extended discrete space which provide paradigmatic examples of nonlinear phenomena. Their stochastic generalizations, i.e., Probabilistic Cellular Automata, are discrete time Markov chains on lattice with finite single--cell states whose distinguishing feature is the \textit{parallel} character of the updating rule. We review some of the results obtained about the metastable behavior of Probabilistic Cellular Automata and we try to point out difficulties and peculiarities with respect to standard Statistical Mechanics Lattice models.