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DTSTART:20190331T030000
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DTSTART:20191027T020000
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DTSTAMP:20260403T220349Z
UID:5cb43c00ae27d066800203@ist.ac.at
DTSTART:20190521T173000
DTEND:20190521T183000
DESCRIPTION:Speaker: Aran Raoufi\nhosted by M. Beiglböck\, N. Berestycki\,
  L. Erdös\, J. Maas\nAbstract: Let $G$ be a bounded-degree infinite graph
 \, and $p_c$ be the critical parameter of bond percolation on $G$. That is
  $p_c$ is the infimum of values of $p$ that you have an infinite cluster a
 lmost surely.In this talk\, we prove that if the isoperimetric dimension o
 f $G$ is higher than 4\, then $p_c(G)<1$. The theorem settles affirmativel
 y two conjectures of Benjamini and Schramm. Notably\, if $G$ is a transiti
 ve graph with super-linear growth\, then $p_c(G) <1$. In particular\, it i
 mplies that if $G$ is a Cayley graph of a finitely generated group without
  a finite index cyclic subgroup\, then $p_c(G)<1$.The proof of the theorem
  starts with the existence of an infinite cluster for percolation in a cer
 tain in-homogeneous random environment governed by the Gaussian free field
 . Then\, by the help of a multiscale decomposition of GFF\, we relate the 
 existence of an infinite cluster in percolation in the random environment 
 to that of percolation with a fix parameter $p<1$.This talk is based on a 
 joint work with H. Duminil-Copin\, S. Goswami\, F. Severo\, and A. Yadin.
LOCATION:Big Seminar room Ground floor / Office Bldg West (I21.EG.101)\, IS
 TA
ORGANIZER:boosthui@ist.ac.at
SUMMARY:Aran Raoufi: Percolation Phase Transition via the Gaussian Free Fie
 ld
URL:https://talks-calendar.ista.ac.at/events/1927
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