BRUNET-DERRIDA PARTICLE SYSTEMS, FREE BOUNDARY PROBLEMS AND WIENER-HOPF EQUATIONS
成果类型：
Article
署名作者：
Durrett, Rick; Remenik, Daniel
署名单位：
Duke University; University of Toronto
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/10-AOP601
发表日期：
2011
页码：
2043-2078
关键词：
摘要：
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 particle is erased, keeping the number of particles constant. We show that, as N -> 8, the empirical measure process associated 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 solution 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 obtained by ignoring the removal of the leftmost particles in our process. The traveling wave solutions correspond to solutions of Wiener-Hopf equations.
来源URL：