Bootstrap percolation is local.
Bootstrap percolation is a classical statistical physics model displaying metastable behaviour. Let each site of the square lattice be infected independently with a fixed probability. At each round, infect each site with at least two infected neighbours and do not remove any infections. How long does it take before the origin is infected? We start by reviewing the rich history of this problem and some of the classical arguments used to tackle it. We then give a very precise answer to the above question in the relevant regime of sparse infection. The key to the proof is a new locality approach to bootstrap percolation, which also solves the bootstrap percolation paradox concerning the failure of numerical predictions in the field.
The talk is based on joint work with Augusto Teixeira available at https://arxiv.org/abs/2404.07903.
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