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Ecological equilibrium for restrained branching random walks

Daniela Bertacchi·Gustavo Posta·Fabio Zucca
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Abstract

We study a generalized branching random walk where particles breed at a rate which depends on the number of neighboring particles. Under general assumptions on the breeding rates we prove the existence of a phase where the population survives without exploding. We construct a nontrivial invariant measure for this case.

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Daniela Bertacchi, Gustavo Posta, Fabio Zucca. 2007-10-19. Ecological equilibrium for restrained branching random walks. https://doi.org/10.1214/105051607000000203

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