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.
Rank dependent branching-selection particle systems.Elec- tronic Journal of Probability, 26
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Branching Brownian motion with rank-based selection and reaction-diffusion equations
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.