Brunet–Derrida particle systems, free boundary problems and Wiener–Hopf equations
By R. Durrett, Daniel Remenik. 2009
63 citations recorded by the source corpus.
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 → ∞, the empirical measure process associated to the system converges in distribution to a deterministic measure-valued 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 Wiener-Hopf equations.
Subfields: Mathematical Physics, Molecular Biology
View Paper: https://www.semanticscholar.org/paper/6856c679b7ac13675b8230c67fb1d88fcf940bf5
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In Mathematical Physics
In Molecular Biology
Citations in the corpus
- Branching random walks (2015, background): “In particular, the weak convergence of the empirical measure of the N -BBM (the analogue of the N -BRW for branching Brownian motion) is proved in [104].”