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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
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
