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We study a particle system in which particles reproduce, move randomly in space, and compete with each other. We prove global survival and determine the asymptotic spread of the population, when the norm of the competition kernel is sufficiently small. In contrast to most previous work, we allow the competition kernel to have an arbitrary, or 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.
Based on joint work with Pascal Maillard.
