University of Cambridge > Talks.cam > Probability > Brunet-Derrida particle systems, free boundary problems and Wiener-Hopf equations

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

Add to your list(s) Download to your calendar using vCal

If you have a question about this talk, please contact Berestycki.

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 tends to infinity, 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. This is joint work with Rick Durrett.

This talk is part of the Probability series.

Tell a friend about this talk:

This talk is included in these lists:

Note that ex-directory lists are not shown.

 

© 2006-2019 Talks.cam, University of Cambridge. Contact Us | Help and Documentation | Privacy and Publicity