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VERSION:2.0
PRODID:icalendar-ruby
CALSCALE:GREGORIAN
X-WR-CALNAME:Probability Seminar
X-WR-TIMEZONE:Eastern Time (US & Canada)
BEGIN:VEVENT
DTSTAMP:20261006T032221Z
UID:tag:localist.com\,2008:EventInstance_47446152838806
DTSTART:20240923T201500Z
DTEND:20240923T211500Z
DESCRIPTION:Speaker: Sahar Diskin (Tel-Aviv University)\n\nTitle: Component
  sizes in percolation on finite regular graphs\n\nAbstract:\n\nA classical
  result by Erdős and Rényi from 1960 shows that the binomial random grap
 h G(n\, p)\nundergoes a fundamental phase transition in its component stru
 cture when the expected average degree is around 1 (i.e.\, around p = 1/n)
 . Specifically\, for p = (1 − ϵ)/n\, where ϵ > 0 is a\nconstant\, all 
 connected components are typically logarithmic in n\, whereas for p = (1 +
  ϵ)/n a\nunique giant component of linear order emerges\, and all other c
 omponents are of order at most logarithmic in n.\n\n\nA similar phenomenon
  — the typical emergence of a unique giant component surrounded\nby comp
 onents of at most logarithmic order — has been observed in random subgra
 phs Gp of\nspecific host graphs G\, such as the d-dimensional binary hyper
 cube\, random d-regular graphs\,\nand pseudo-random (n\, d\, λ)-graphs\, 
 though with quite different proofs.\n\n\nThis naturally leads to the quest
 ion: What assumptions on a d-regular n-vertex graph G suffice\nfor its ran
 dom subgraph to typically exhibit this phase transition around a critical 
 probability\np = 1/(d − 1)? Furthermore\, is there a unified approach th
 at encompasses these classical cases? In this talk\, we demonstrate that i
 t suffices for G to have mild global edge expansion and (almost-optimal) e
 xpansion of sets of (poly-)logarithmic order in n. This result covers many
  previously considered concrete setups.\n\n \n\nWe also discuss the tightn
 ess of our sufficient conditions.\n\n \n\nJoint work with Michael Krivelev
 ich.
GEO:42.358262;-71.090045
LOCATION:Building 2\, 143
SUMMARY:Probability Seminar
URL;VALUE=URI:https://calendar.mit.edu/event/probability-seminar-4022
CATEGORIES:Conferences/Seminars/Lectures
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