Article Dans Une Revue Journal of the London Mathematical Society Année : 2024

Branching random walk with non-local competition

Résumé

We study the Bolker-Pacala-Dieckmann-Law (BPDL) model of population dynamics in the regime of large population density. The BPDL model is a particle system in which particles reproduce, move randomly in space, and compete with each other locally. We rigorously prove global survival as well as a shape theorem describing the asymptotic spread of the population, when the population density is sufficiently large. In contrast to most previous studies, we allow the competition kernel to have an arbitrary, even infinite range, whence the term non-local competition. This makes the particle system non-monotone and of infinite-range dependence, meaning that the usual comparison arguments break down and have to be replaced by a more hands-on approach. Some ideas in the proof are inspired by works on the non-local Fisher-KPP equation, but the stochasticity of the model creates new difficulties.

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hal-03793092 , version 1 (07-07-2025)

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Pascal Maillard, Sarah Penington. Branching random walk with non-local competition. Journal of the London Mathematical Society, 2024, 109 (6), ⟨10.1112/jlms.12919⟩. ⟨hal-03793092⟩
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