Math @ Duke

Publications [#243521] of Richard T. Durrett
Papers Published
 Durrett, R; Remenik, D, Brunet–Derrida particle systems, free boundary problems and Wiener–Hopf equations,
The Annals of Probability, vol. 39 no. 6
(November, 2011),
pp. 20432078, ISSN 00911798 [doi]
(last updated on 2018/08/19)
Abstract: We consider a branchingselection system in ℝ with N particles which give birth independently at rate 1 and where after each birth the leftmost particle is erased, keeping the number of particles constant. We show that, as N →∞, the empirical measure process associated to the system converges in distribution to a deterministic measurevalued process whose densities solve a free boundary integrodifferential equation. We also show that this equation has a unique traveling wave solution traveling at speed c or no such solution depending on whether c ≥ a or c>a,wherea is the asymptotic speed of the branching random walk obtained by ignoring the removal of the leftmost particles in our process. The traveling wave solutions correspond to solutions of WienerHopf equations. © 2011 Institute of Mathematical Statistics.


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