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.
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