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SUMMARY:Percolation through isoperimetry - Michael Krivelevich (Tel Aviv)
DTSTART:20240530T133000Z
DTEND:20240530T143000Z
UID:TALK216931@talks.cam.ac.uk
CONTACT:103978
DESCRIPTION:Let G be a d-regular graph of growing degree on n vertices\, a
 nd form a random subgraph G_p of G by retaining edge of G independently wi
 th probability p=p(d). Which conditions on G suffice to observe a phase tr
 ansition at p=1/d\, similar to that in the binomial random graph G(n\,p)\,
  or\, say\, in a random subgraph of the binary hypercube Q^d?\n\nWe argue 
 that in the supercritical regime p=(1+epsilon)/d\, epsilon>0 being a small
  constant\, postulating that every vertex subset S of G of at most n/2 ver
 tices has its edge boundary at least C|S|\, for some large enough constant
  C=C(\\epsilon)>0\, suffices to guarantee the likely appearance of the gia
 nt component in G_p. Moreover\, its asymptotic order is equal to that in t
 he random graph G(n\,(1+\\epsilon)/n)\, and all other components are typic
 ally much smaller.\n\nWe further give examples demonstrating the tightness
  of this result in several key senses.\n\nThis is joint work with Sahar Di
 skin\, Joshua Erde and Mihyun Kang.
LOCATION:MR12
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