Anchored expansion in supercritical percolation on nonamenable graphs
Let G be a transitive nonamenable graph, and consider supercritical Bernoulli bond percolation on G. We prove that the probability that the origin lies in a finite cluster of size n decays exponentially in n. We deduce that:

1. Every infinite cluster has anchored expansion almost surely. This answers positively a question of Benjamini, Lyons, and Schramm (1997).

2. Various observables, including the percolation probability and the truncated susceptibility are analytic functions of p throughout the entire supercritical phase.

Joint work with Tom Hutchcroft.
Date: 7 May 2019, 12:00 (Tuesday, 2nd week, Trinity 2019)
Venue: Mathematical Institute, Woodstock Road OX2 6GG
Speaker: Jonathan Hermon (University of Cambridge)
Organising department: Department of Statistics
Organisers: Christina Goldschmidt (Department of Statistics, University of Oxford), James Martin (Department of Statistics, University of Oxford)
Part of: Probability seminar
Booking required?: Not required
Audience: Public
Editor: Christina Goldschmidt