Ancestral lineages for a branching annihilating random walk

Pascal Oswald

Stochastic Processes and their Applications, 2025, vol. 187, issue C

Abstract: We study the ancestral lineages of individuals of a stationary discrete-time branching annihilating random walk (BARW) on the d-dimensional lattice Zd. Each individual produces a Poissonian number of offspring with mean μ which then jump independently to a uniformly chosen site with a fixed distance R of their parent. Should two or more particles jump to the same site, all particles at that site get annihilated. By interpreting the ancestral lineage of such an individual as a random walk in a dynamical random environment, we obtain a law of large numbers and a functional central limit theorem for the ancestral lineage whenever the model parameters satisfy μ∈(1,e2) and R=R(μ) is large enough.

Keywords: Branching annihilating random walk; Ancestral lineages; Random walk in dynamic random environment (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spa.2025.104648

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