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SUMMARY:Anchored expansion in supercritical percolation on nonamenable gra
phs - Jonathan Hermon (University of Cambridge)
DTSTART;VALUE=DATE-TIME:20190507T120000
DTEND;VALUE=DATE-TIME:20190507T130000
UID:https://talks.ox.ac.uk/talks/id/1fa9bea7-0fa5-4981-a842-26111ed1dcba/
DESCRIPTION:Let G be a transitive nonamenable graph\, and consider supercr
itical 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: \n\n1. Every infinite cluster has anchored expansion almos
t surely. This answers positively a question of Benjamini\, Lyons\, and Sc
hramm (1997). \n\n2. Various observables\, including the percolation proba
bility and the truncated susceptibility are analytic functions of p throug
hout the entire supercritical phase.\n\nJoint work with Tom Hutchcroft. \n
Speakers:\nJonathan Hermon (University of Cambridge)
LOCATION:Mathematical Institute\, Woodstock Road OX2 6GG
URL:https://talks.ox.ac.uk/talks/id/1fa9bea7-0fa5-4981-a842-26111ed1dcba/
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DESCRIPTION:Talk:Anchored expansion in supercritical percolation on noname
nable graphs - Jonathan Hermon (University of Cambridge)
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