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SUMMARY:First passage percolation in hostile environment (on hyperbolic gr
 aphs) - Elisabetta Candellero (Warwick)
DTSTART:20180508T130000Z
DTEND:20180508T140000Z
UID:TALK97885@talks.cam.ac.uk
CONTACT:Perla Sousi
DESCRIPTION:We consider two first-passage percolation processes FPP_1 and 
 FPP_{\\lambda}\, spreading with rates 1 and \\lambda > 0 respectively\, on
  a non-amenable hyperbolic graph G with bounded degree. FPP_1 starts from 
 a single source at the origin of G\, while the initial con figuration of F
 PP_{\\lambda} consists of countably many seeds distributed according to a 
 product of iid Bernoulli random variables of parameter \\mu > 0 on V (G)\\
 {o}. Seeds start spreading FPP_{\\lambda} after they are reached by either
  FPP_1 or FPP_{\\lambda}. We show that for any such graph G\, and any fixe
 d value of \\lambda > 0 there is a value \\mu_0 = \\mu_0(G\,\\lambda ) > 0
  such that for all 0 < \\mu < \\mu_0 the two processes coexist with positi
 ve probability. This shows a fundamental difference with the behavior of s
 uch processes on Z^d. (Joint work with Alexandre Stauffer.)\n
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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