Ecological equilibrium for restrained branching random walks

Mathematics – Probability

Scientific paper

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Published in at http://dx.doi.org/10.1214/105051607000000203 the Annals of Applied Probability (http://www.imstat.org/aap/) by

Scientific paper

10.1214/105051607000000203

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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