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SUMMARY:Brunet-Derrida particle systems\, free boundary problems and Wiene
 r-Hopf equations - Daniel Remenik\, Cornell University
DTSTART:20100112T163000Z
DTEND:20100112T173000Z
UID:TALK22459@talks.cam.ac.uk
CONTACT:Berestycki
DESCRIPTION:We consider a branching-selection system in $\\R$ with N parti
 cles which give birth independently at rate 1 and where after each birth t
 he leftmost particle is erased\, keeping the number of particles constant.
  We show that\, as N tends to infinity\, the empirical measure process ass
 ociated to the system converges in distribution to a deterministic measure
 -valued process whose densities solve a free boundary integro-differential
  equation. We also show that this equation has a unique traveling wave sol
 ution traveling at speed c or no such solution depending on whether c >= a
  or c < a\, where a is the asymptotic speed of the branching random walk o
 btained by ignoring the removal of the leftmost particles in our process. 
 The traveling wave solutions correspond to solutions of Wiener-Hopf equati
 ons. This is joint work with Rick Durrett. 
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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