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SUMMARY:Forest fire processes and near-critical percolation with heavy-tai
 led impurities - Pierre Nolin (City University of Hong Kong)
DTSTART:20191029T140000Z
DTEND:20191029T150000Z
UID:TALK131458@talks.cam.ac.uk
CONTACT:Perla Sousi
DESCRIPTION:We discuss models of forest fires (or epidemics): on a given p
 lanar lattice\, all vertices are initially vacant\, and then become occupi
 ed at rate 1. If an occupied vertex is hit by lightning\, which occurs at 
 a (typically very small) rate\, all the vertices connected to it burn imme
 diately\, i.e. they become vacant. We want to analyze the behavior of such
  processes near and beyond the critical time (i.e. the time after which\, 
 in the absence of fires\, infinite connected components would emerge).\n\n
 We are led to introduce a percolation model where regions ("impurities") o
 f the lattice are first removed\, in an independent fashion. These impurit
 ies are not only microscopic\, but also allowed to be mesoscopic. We are i
 nterested in whether\, on the randomly perforated lattice\, the connectivi
 ty properties of percolation remain of the same order as without impuritie
 s\, for values of the percolation parameter close to the critical value. T
 his generalizes a celebrated result by Kesten for near-critical percolatio
 n (that can be viewed as critical percolation with single-site impurities)
 .\n\nThis talk is based on a joint work with Rob van den Berg (CWI and VU\
 , Amsterdam).
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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