# Supercritical percolation on finite transitive graphs

## Location

Zoom

Monday, February 22, 2021 11:00 AM

Tom Hutchcroft (Cambridge)

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.