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SUMMARY:A sharp threshold technique for percolation on transitive graphs
DTSTART;VALUE=DATE-TIME:20230105T130000Z
DTEND;VALUE=DATE-TIME:20230105T140000Z
DTSTAMP;VALUE=DATE-TIME:20230324T183100Z
UID:indico-event-8294@indico.math.cnrs.fr
DESCRIPTION:Speakers: Philip Easo (California Institute of Technology)\n\n
Tom Hutchcroft and I have been working to develop a general theory of perc
olation on arbitrary finite transitive graphs. We have had to apply tools
from the study of percolation on infinite transitive graphs (traditionally
studied by "probabilists") to percolation on high-degree finite graphs (t
raditionally studied by "combinatorialists") and vice versa. In this prese
ntation\, I would like to advertise a tool that we have brought back from
the high-degree setting. It is a new way to apply a sharp threshold result
originally due to Bourgain then sharpened by Hatami. I will explain how t
his tool can be applied to give a very short proof of a new result in the
setting of percolation on infinite transitive graphs\, namely that in the
supercritical phase\, the infinite cluster density `theta' is determined b
y the (Benjamini-Schramm) local geometry of the underlying graph.\n\nhttps
://indico.math.cnrs.fr/event/8294/
URL:https://indico.math.cnrs.fr/event/8294/
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