OxTalks is Changing
OxTalks will soon be transitioning to Oxford Events (full details are available on the Staff Gateway). A two-week publishing freeze is expected to start before the end of Hilary Term to allow all future events to be migrated to the new platform. During this period, you will not be able to submit or edit events on OxTalks. The exact freeze dates will be confirmed on the Staff Gateway and via email to identified OxTalks users.
If you have any questions, please contact halo@digital.ox.ac.uk
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
