Probability Seminar: Supercritical percolation on finite transitive graphs

Supercritical percolation on finite transitive graphs
Monday, February 22, 2021 - 11:00am
Tom Hutchcroft (Cambridge)
Abstract / Description: 

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.

The Probability Seminars for Winter Quarter will be held online via Zoom at 11am on Mondays. Please note that these events will be locked by the Host after ten minutes, so latecomers will not be able to join the Meeting. Subscribe to our distribution list to receive Meeting IDs and passwords via email.