BEGIN:VCALENDAR
VERSION:2.0
PRODID:www.imperial.ac.uk
BEGIN:VEVENT
UID:5ece98c8c8a29
DTSTART:20200303T150000Z
SEQUENCE:0
TRANSP:OPAQUE
DTEND:20200303T160000Z
URL:https://www.imperial.ac.uk/events/115827/christina-goldschmidt-oxford-t
he-scaling-limit-of-a-critical-random-directed-graph/
LOCATION:Room 341\, Huxley Building\, South Kensington Campus\, Imperial Co
llege London\, London\, SW7 2AZ\, United Kingdom
SUMMARY:Christina Goldschmidt (Oxford ): The scaling limit of a critical ra
ndom directed graph
CLASS:PUBLIC
DESCRIPTION:Stochastic Analysis Seminar\n \nAbstract:\nWe consider the ran
dom directed graph D(n\, p) with vertex set {1\, 2\, . . . \, n} in whi
ch each of the n(n − 1) possible directed edges is present independent
ly with probability p. We are interested in the strongly connected compone
nts of this directed graph. A phase transition for the emergence of a gi
ant strongly connected component is known to occur at p = 1/n\, with criti
cal window p = 1/n + \\lambda n^{-4/3} for \\lambda \\in \\R. We show that
\, within this critical window\, the strongly connected components of D(n\
, p)\, ranked in decreasing order of size and rescaled by n^{-1/3}\, conve
rge in distribution to a sequence of finite strongly connected directed
multigraphs with edge lengths which are either 3-regular or loops. This
is joint work with Robin Stephenson (Sheffield).
X-ALT-DESC;FMTTYPE=text/html:*Stochastic Analysis Seminar*

\n<
p> \n### Abstract:

\nWe consider the
random directed graph D(n\, p) with vertex set {1\, 2\, . . . \, n} in
which each of the n(n − 1) possible directed edges is present indepen
dently with probability p. We are interested in the strongly connected com
ponents of this directed graph. A phase transition for the emergence of
a giant strongly connected component is known to occur at p = 1/n\, with c
ritical window p = 1/n + \\lambda n^{-4/3} for \\lambda \\in \\R. We show
that\, within this critical window\, the strongly connected components of
D(n\, p)\, ranked in decreasing order of size and rescaled by n^{-1/3}\, c
onverge in distribution to a sequence of finite strongly connected direct
ed multigraphs with edge lengths which are either 3-regular or loops. T
his is joint work with Robin Stephenson (Sheffield).

DTSTAMP:20200527T164352Z
END:VEVENT
END:VCALENDAR