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CATEGORIES:Probability
SUMMARY:Asymptotic behaviour of near-critical branching Br
ownian motion - NathanaĆ«l Berestycki (Cambridge)
DTSTART;TZID=Europe/London:20100504T163000
DTEND;TZID=Europe/London:20100504T173000
UID:TALK24733AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/24733
DESCRIPTION:Consider a system of particles that perform branch
ing Brownian motion with negative drift \\sqrt(2-
\\eps) and are killed upon hitting zero. Initially
\, there is just one particle at x. Kesten (1978)
proved that the system survives if and only if \\e
ps>0. In this talk I shall describe recent joint w
ork with Julien Berestycki and Jason Schweinsberg
concerning the limiting behaviour of this process
as \\eps tends to 0. In particular we establish sh
arp asymptotics for the limiting survival probabil
ity as a function of the starting point x. Moreove
r\, the limiting genealogy between individuals fro
m this population is shown to have a characteristi
c time scale of order \\eps^{-3/2}. When time is m
easured in these units we show that the geometry o
f the genealogical tree converges to the Bolthause
n-Sznitman coalescent. This is closely related to
a set of conjectures by Brunet\, Derrida and Simon
.
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0W
B
CONTACT:HoD Secretary\, DPMMS
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