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SUMMARY:Supercritical Percolation on Finite Transitive Graphs - Philip Eas
 o (Cambridge)
DTSTART:20210316T140000Z
DTEND:20210316T150000Z
UID:TALK158326@talks.cam.ac.uk
CONTACT:Perla Sousi
DESCRIPTION:Consider a large\, finite graph. In bond percolation\, each ed
 ge is independently set to "open" with probability p. In many cases\, when
  we increase the parameter p across a narrow critical window\, the subgrap
 h of open edges undergoes a phase transition. With high probability\, belo
 w the window\, there are no giant components\, whereas above the window\, 
 there is at least one giant component. We prove that for transitive graphs
  above the window\, there is exactly one giant component\, with high proba
 bility. This was conjectured to hold by Benjamini\, but was only known for
  large tori and expanders\, using methods specific to those cases.\n\nThe 
 work that I will describe is joint with Tom Hutchcroft.
LOCATION:Zoom
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