Bootstrap percolation, and other automata. (December 2017)

• Record Type: Journal Article
• Authors: Morris, Robert
• Is Part Of: European journal of combinatorics. Volume 66(2017)
• Page Start: 250
• Page End: 263
• Publication Date: 2017-12
• Subjects: Combinatorial analysis -- Periodicals; Analyse combinatoire -- Périodiques; Combinatorial analysis; Periodicals; Electronic journals; 511.6
• DOI: 10.1016/j.ejc.2017.06.024
• Languages: English
• ISSNs: 0195-6698

Abstract

Abstract: Many fundamental and important questions from statistical physics lead to beautiful problems in extremal and probabilistic combinatorics. One particular example of this phenomenon is the study of bootstrap percolation, which is motivated by a variety of 'real-world' cellular automata, such as the Glauber dynamics of the Ising model of ferromagnetism, and kinetically constrained spin models of the liquid–glass transition. In this review article, we will describe some dramatic recent developments in the theory of bootstrap percolation (and, more generally, of monotone cellular automata with random initial conditions), and discuss some potential extensions of these methods and results to other automata. In particular, we will state numerous conjectures and open problems.