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SUMMARY:Percolation on hyperbolic groups - Tom Hutchcroft (Cambridge)
DTSTART:20181123T134500Z
DTEND:20181123T144500Z
UID:TALK110767@talks.cam.ac.uk
CONTACT:Richard Webb
DESCRIPTION:In Bernoulli bond percolation\, the edges of a graph are eithe
 r deleted or retained independently at random\, with retention probability
  p. As p changes\, the geometry of the retained subgraph is expected to un
 dergo one or more abrupt changes at special values of p\, known as phase t
 ransitions. Although traditionally studied primarily on Euclidean lattices
 \, the study of percolation on more general graphs\, and in particular on 
 general Cayley graphs\, has been popular since the 90's and has revealed s
 everal connections between probability and geometric group theory. A centr
 al 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 infinite 
 connected components almost surely. The goal of my talk is to survey what 
 has been done on this problem and to discuss my recent proof that the conj
 ecture is true for hyperbolic groups.
LOCATION:CMS\, MR13
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