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SUMMARY:The depth first search exploration of a supercritical configuratio
n model - Laurent Ménard (Université Paris Nanterre)
DTSTART;VALUE=DATE-TIME:20191121T100000Z
DTEND;VALUE=DATE-TIME:20191121T110000Z
UID:https://talks.ox.ac.uk/talks/id/b99e823e-182d-4f5e-88be-387c8632ce72/
DESCRIPTION:We consider large random graphs with a given degree sequence.
In the sparse regime where the degree sequence converges to a probability
distribution\, the model has a phase transition for the existence of a mac
roscopic connected component. In this talk\, we will study the depth first
search algorithm in the supercritical regime. In particular\, we will see
that the evolution of the empirical degree distribution of the unexplored
vertices has a fluid limit which is driven by an infinite system of diffe
rential equations. Surprisingly\, this system admits an explicit solution
in terms of the initial degree distribution. This in turn allows to prove
that the renormalised contour process of the exploration has a determinist
ic profile for which we can give an explicit parametric representation. Th
e height of this curve gives information about long simple paths in the gr
aph.\nSpeakers:\nLaurent Ménard (Université Paris Nanterre)
LOCATION:24-29 St Giles' (Department of Statistics\, LG.01 (Large Lecture
Theatre))\, 24-29 St Giles' OX1 3LB
URL:https://talks.ox.ac.uk/talks/id/b99e823e-182d-4f5e-88be-387c8632ce72/
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DESCRIPTION:Talk:The depth first search exploration of a supercritical con
figuration model - Laurent Ménard (Université Paris Nanterre)
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