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SUMMARY:Christina Goldschmidt (University of Oxford)
DTSTART:20200511T133000Z
DTEND:20200511T140000Z
DTSTAMP:20260423T052545Z
UID:LPDD/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LPDD/6/">The
  scaling limit of a critical random directed graph</a>\nby Christina Golds
 chmidt (University of Oxford) as part of Les probabilités de demain webin
 ar\n\n\nAbstract\nWe consider the random directed graph $D(n\, p)$ with ve
 rtex set $\\{1\, 2\, \\ldots\, n\\}$ in which each of the $n(n − 1)$ pos
 sible directed edges is present independently with probability $p$. We are
  interested in the strongly connected components of this directed graph. A
  phase transition for the emergence of a giant strongly connected componen
 t is known to occur at $p = 1/n$\, with critical window $p = 1/n + \\lambd
 a n^{-4/3}$ for $\\lambda \\in \\R$. We show that\, within this critical w
 indow\, the strongly connected components of $D(n\, p)$\, ranked in decrea
 sing order of size and rescaled by $n^{-1/3}$\, converge in distribution t
 o a sequence of finite strongly connected directed multigraphs with edge l
 engths which are either 3-regular or loops.\n\nThis is joint work with Rob
 in Stephenson (University of Sheffield).\n
LOCATION:https://researchseminars.org/talk/LPDD/6/
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