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Universality for bootstrap percolation

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  • UserRob Morris (IMPA)
  • ClockWednesday 01 May 2024, 14:30-15:30
  • HouseMR12.

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In this talk I will give an overview of the proof of the “Universality Conjecture” for general bootstrap percolation models. Roughly speaking, the conjecture states that every d-dimensional monotone cellular automaton is a member of one of d+1 universality classes, which are characterized by their behaviour on sparse random sets. More precisely, it states that if sites of the lattice Z^d are initially infected independently with probability p, then the expected infection time of the origin is either infinite, or is a tower of height r for some r \in {1,...,d}. I will also describe an uncomputability result regarding the exponent of p at the top of the tower.

Based on joint work with Paul Balister, Béla Bollobás and Paul Smith.

This talk is part of the Combinatorics Seminar series.

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