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CATEGORIES:Probability
SUMMARY:Supercritical Percolation on Finite Transitive Gra
phs - Philip Easo (Cambridge)
DTSTART;TZID=Europe/London:20210316T140000
DTEND;TZID=Europe/London:20210316T150000
UID:TALK158326AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/158326
DESCRIPTION:Consider a large\, finite graph. In bond percolati
on\, each edge is independently set to "open" with
probability p. In many cases\, when we increase t
he parameter p across a narrow critical window\, t
he subgraph of open edges undergoes a phase transi
tion. With high probability\, below the window\, t
here are no giant components\, whereas above the w
indow\, there is at least one giant component. We
prove that for transitive graphs above the window\
, there is exactly one giant component\, with high
probability. This was conjectured to hold by Benj
amini\, but was only known for large tori and expa
nders\, using methods specific to those cases.\n\n
The work that I will describe is joint with Tom Hu
tchcroft.
LOCATION:Zoom
CONTACT:Perla Sousi
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