Overview: PCA Models and Issues

Probabilistic cellular automata (PCA) are interacting discrete stochastic dynamical systems used as a modeling tool for a wide range of natural and societal phenomena. Their key features are: (i) a stochastic component that distinguishes them from the well-known cellular automata (CA) algorithms and (ii) an underlying parallelism that sets them apart from purely asynchronous simulation dynamics in statistical mechanics, such as interacting particle systems and Glauber dynamics. On the applied side, these features make PCA an attractive computational framework for high-performance computing, distributed computing, and simulation. Indeed, PCA have been put to good use as part of multiscale simulation frameworks for studying natural systems or large interconnected network structures. On the mathematical side, PCA have a rich mathematical theory that leads to a better understanding of the role of randomness and synchronicity in the evolution of large systems. This book is an attempt to present a wide panorama of the current status of PCA theory and applications. Contributions cover important issues and applications in probability, statistical mechanics, computer science, natural sciences, and dynamical systems. This initial chapter is intended both as a guide and an introduction to the issues discussed in the book. The chapter starts with a general overview of PCA modeling, followed by a presentation of conspicuous applications in different contexts. It closes with a discussion of the links between approaches and perspectives for future developments.