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UID:8120@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20150327T110000
DTEND;TZID=Europe/Paris:20150327T120000
DTSTAMP:20241120T210035Z
URL:https://www.i2m.univ-amu.fr/evenements/percolation-on-the-stationary-d
 istribution-of-the-voter-model-on-zd-daniel-valesin/
SUMMARY:Daniel Valesin (University of Groningen): Percolation on the statio
 nary distribution of the voter model on Z^d - Daniel Valesin
DESCRIPTION:Daniel Valesin: The voter model on $\\Z^d$ is a particle system
  that serves as a rough model for changes of opinions among social agents 
 or\, alternatively\, competition between biological species occupying spac
 e. When the model is considered in dimension 3 or higher\, its set of (ext
 remal) stationary distributions is equal to a family of measures $\\mu_\\a
 lpha$\, for $\\alpha$ between 0 and 1. A configuration sampled from $\\mu_
 alpha$ is a field of 0's and 1's on $\\Z^d$ in which the density of 1's is
  $\\alpha$. We consider such a configuration from the point of view of sit
 e percolation on $\\Z^d$. We prove that in dimensions 5 and higher\, the p
 robability of existence of an infinite percolation cluster exhibits a phas
 e transition in $\\alpha$. If the voter model is allowed to have long rang
 e\, we prove the same result for dimensions 3 and higher. Joint work with 
 Balázs Ráth.\n\n\n
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 020/01/Daniel_Valesin.jpg
CATEGORIES:Séminaire,Probabilités
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