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SUMMARY:Coexistence of competing first passage percolation on hyperbolic g
raphs
DTSTART;VALUE=DATE-TIME:20181108T130000Z
DTEND;VALUE=DATE-TIME:20181108T140000Z
DTSTAMP;VALUE=DATE-TIME:20200403T055522Z
UID:indico-event-3823@indico.math.cnrs.fr
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\nhttps://ind
ico.math.cnrs.fr/event/3823/
LOCATION:ICJ\, La Doua Fokko du Cloux
URL:https://indico.math.cnrs.fr/event/3823/
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