Ancestral lineages for a branching annihilating random walk

2024/03/28 by Pascal Oswald, Oswald, Pascal
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #60K35 (Primary) #92D25 (Secondary) #Algorithms and Data Compression #DNA and Biological Computing #FOS: Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2403.19483

openalex publication_date 2024/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study ancestral lineages of individuals of a stationary discrete-time branching annihilating random walk (BARW) on the d-dimensional lattice ℤ^d. 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. 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.

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