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ThursdayJul 25, 201913:30

Geometric Functional Analysis and Probability SeminarRoom 155

Speaker:Jonathan Hermon Title:Anchored expansion in supercritical percolation on nonamenable graphs.Abstract:opens in new windowin html pdfopens in new windowLet 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:

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