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Ancestral lineages for a branching annihilating random walk (2403.19483v1)

Published 28 Mar 2024 in math.PR

Abstract: We study ancestral lineages of individuals of a stationary discrete-time branching annihilating random walk (BARW) on the $d$-dimensional lattice $\mathbb{Z}d$. Each individual produces a Poissonian number of offspring with mean $\mu$ 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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References (11)
  1. Local limit theorems for a directed random walk on the backbone of a supercritical oriented percolation cluster. Electron. J. Probab., 28:Paper No. 37, 54, 2023.
  2. Survival and complete convergence for a branching annihilating random walk. arXiv preprint arXiv:2304.09127v2, 2023.
  3. Random walks in dynamic random environments and ancestry under local population regulation. Electron. J. Probab., 21:Paper No. 38, 43, 2016.
  4. Directed random walk on the backbone of an oriented percolation cluster. Electron. J. Probab., 18:no. 80, 35, 2013.
  5. Survival and complete convergence for a spatial branching system with local regulation. The Annals of Applied Probability, 17(5-6):1777–1807, 2007.
  6. Ancestral lineages in spatial population models with local regulation. In Probabilistic structures in evolution, EMS Ser. Congr. Rep., pages 291–310. EMS Press, Berlin, [2021] ©2021.
  7. Looking forwards and backwards: dynamics and genealogies of locally regulated populations, 2023.
  8. Alison Etheridge. Some mathematical models from population genetics, volume 2012 of Lecture Notes in Mathematics. Springer, Heidelberg, 2011. Lectures from the 39th Probability Summer School held in Saint-Flour, 2009, École d’Été de Probabilités de Saint-Flour. [Saint-Flour Probability Summer School].
  9. Katja Miller. Erratum to: “Random walks on weighted, oriented percolation clusters” [MR3460870]. ALEA Lat. Am. J. Probab. Math. Stat., 14(1):173–175, 2017.
  10. Katja Miller. Random walks on oriented percolation and in recurrent environments. PhD thesis, Technische Universität München, 2017.
  11. Around probabilistic cellular automata. Theoretical Computer Science, 559:42–72, 2014.

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