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CATEGORIES:Geometric Group Theory (GGT) Seminar
SUMMARY:Percolation on hyperbolic groups - Tom Hutchcroft
(Cambridge)
DTSTART;TZID=Europe/London:20181123T134500
DTEND;TZID=Europe/London:20181123T144500
UID:TALK110767AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/110767
DESCRIPTION:In Bernoulli bond percolation\, the edges of a gra
ph are either deleted or retained independently at
random\, with retention probability p. As p chang
es\, the geometry of the retained subgraph is expe
cted to undergo one or more abrupt changes at spec
ial values of p\, known as phase transitions. Alth
ough traditionally studied primarily on Euclidean
lattices\, the study of percolation on more genera
l graphs\, and in particular on general Cayley gra
phs\, has been popular since the 90's and has reve
aled several connections between probability and g
eometric group theory. A central conjecture in the
area\, due to Benjamini and Schramm\, is that if
G is a Cayley graph of a nonamenable group\, then
there exists an interval of values of p for which
the open subgraph contains infinitely many infinit
e connected components almost surely. The goal of
my talk is to survey what has been done on this pr
oblem and to discuss my recent proof that the conj
ecture is true for hyperbolic groups.
LOCATION:CMS\, MR13
CONTACT:Richard Webb
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