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Supercritical percolation on finite transitive graphs

Monday, February 22, 2021 - 11:00am

Speaker:   Tom Hutchcroft, Cambridge University

Abstract:   In Bernoulli bond percolation, each edge of some graph are chosen to be either deleted or retained independently at random with retention probability p. For many large finite graphs, there is a phase transition such that if p is sufficiently large then there exists a giant cluster whose volume is proportional to that of the graph with high probability. We prove that in this phase the giant cluster must be unique with high probability: this was previously known only for tori and expander graphs via methods specific to those cases. The work that I will describe is joint with Philip Easo.