Low-dimensional lonely branching random walks die out

DOI10.1214/18-AOP1271zbMath1466.60198arXiv1708.06377WikidataQ128315520 ScholiaQ128315520MaRDI QIDQ2414142

Matthias Birkner, Rongfeng Sun

Publication date: 10 May 2019

Published in: The Annals of Probability (Search for Journal in Brave)

Abstract: The lonely branching random walks on ${mathbb Z}^d$ is an interacting particle system where each particle moves as an independent random walk and undergoes critical binary branching when it is alone. We show that if the symmetrized walk is recurrent, lonely branching random walks die out locally. Furthermore, the same result holds if additional branching is allowed when the walk is not alone.

Full work available at URL: https://arxiv.org/abs/1708.06377

zbMATH Keywords

branching random walksself-catalytic branching

Mathematics Subject Classification ID

Interacting particle systems in time-dependent statistical mechanics (82C22) Interacting random processes; statistical mechanics type models; percolation theory (60K35)

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