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CATEGORIES:Probability
SUMMARY:Brunet-Derrida particle systems\, free boundary pr
oblems and Wiener-Hopf equations - Daniel Remenik\
, Cornell University
DTSTART;TZID=Europe/London:20100112T163000
DTEND;TZID=Europe/London:20100112T173000
UID:TALK22459AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/22459
DESCRIPTION:We consider a branching-selection system in $\\R$
with N particles which give birth independently at
rate 1 and where after each birth the leftmost pa
rticle is erased\, keeping the number of particles
constant. We show that\, as N tends to infinity\,
the empirical measure process associated to the s
ystem converges in distribution to a deterministic
measure-valued process whose densities solve a fr
ee boundary integro-differential equation. We also
show that this equation has a unique traveling wa
ve solution traveling at speed c or no such soluti
on depending on whether c >= a or c < a\, where a
is the asymptotic speed of the branching random wa
lk obtained by ignoring the removal of the leftmos
t particles in our process. The traveling wave sol
utions correspond to solutions of Wiener-Hopf equa
tions. This is joint work with Rick Durrett.
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0W
B
CONTACT:Berestycki
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