Department of Mathematics

Details

Brunet-Derrida particle systems, free boundary problems, and Wiener-Hopf equations

by Daniel Remenik | University of Toronto
Time: 16:00  (Monday, Sep. 27, 2010)
Location: Stewart Library, Fields Institute, 222 College St.
Abstract:
We consider a branching-selection system in $\mathbb{R}$ 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 $N\to\infty$, 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 $c\geq a$ 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. Joint work with Rick Durrett.

Dates in this series

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