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.
Bertacchi, D., Posta, G., Zucca, F. (2007). Ecological equilibrium for restrained branching random walks. THE ANNALS OF APPLIED PROBABILITY, 17(4), 1117-1137 [10.1214/105051607000000203].
Ecological equilibrium for restrained branching random walks
BERTACCHI, DANIELA;
2007
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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