Branching Brownian motion with rank-based selection has a hydrodynamic limit given by the reaction-diffusion equation U_t = ½ U_xx + r(t) G(U), and its asymptotic velocity is determined by the PDE's spreading speed under general conditions on the selection function ψ.
Critical Drift for Brownian Bees and a Reflected Brownian Motion Invariance Principle
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The (N,p)-BBM converges in the hydrodynamic limit to a two-sided free boundary problem on a finite interval with p-dependent Neumann and Dirichlet conditions; the limiting velocity is the unique travelling-wave speed of that problem.
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Two-Sided Free Boundary Problems Arising From Branching-Selection Particle Systems
The (N,p)-BBM converges in the hydrodynamic limit to a two-sided free boundary problem on a finite interval with p-dependent Neumann and Dirichlet conditions; the limiting velocity is the unique travelling-wave speed of that problem.