Deterministic growth-dispersal models and branching random walk (Q1895143)

A simplification of the deterministic model of \textit{H. F. Weinberger} [SIAM J. Math. Anal. 13, 353-396 (1982; Zbl 0529.92010)] for growth and dispersion in a biological population is related to the branching random walk, allowing results from one framework to be transferred to the other. The relationship exploited is the same as that between the Fisher (or KPP) equation and branching Brownian motion, but here the models are in discrete-time and on the integer lattice. The connection allows answers to be given to certain questions about the shape and uniqueness of travelling waves for the version of Weinberger's model considered.