BrunetDerrida particle systems, free boundary problems and WienerHopf equations
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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 tends to infinity, 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, 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 WienerHopf equations. This is joint work with Rick Durrett.
This talk is part of the Probability series.
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