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CATEGORIES:Probability
SUMMARY:Coalescing systems of non-Brownian particles - Arn
ab Sen (Cambridge)
DTSTART;TZID=Europe/London:20101102T163000
DTEND;TZID=Europe/London:20101102T173000
UID:TALK26754AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/26754
DESCRIPTION:\nA well-known result of Arratia shows that one ca
n make rigorous the notion of starting an independ
ent Brownian motion at every point of an arbitrary
closed subset of the real line and then building
a set-valued process by requiring particles to coa
lesce when they collide. Arratia noted that the va
lue of this process will be almost surely a locall
y finite set at all positive times\, and a finite
set almost surely if the starting set is compact.
We investigate whether such instantaneous coalesce
nce still occurs for coalescing systems of particl
es where either the state space of the individual
particles is not locally homeomorphic to an interv
al or the sample paths of the individual particles
are discontinuous. We show that Arratia's conclus
ion is valid for Brownian motions on the Sierpinsk
i gasket and for stable processes on the real line
with stable index greater than one. Joint work wi
th Steve Evans and Ben Morris. \n\n\nhttp://www.st
atslab.cam.ac.uk/Dept/People/sen.html
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0W
B
CONTACT:Berestycki
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