The Annals of Probability

Low-dimensional lonely branching random walks die out

Matthias Birkner and Rongfeng Sun

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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.

Article information

Ann. Probab., Volume 47, Number 2 (2019), 774-803.

Received: August 2017
Revised: March 2018
First available in Project Euclid: 26 February 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 82C22: Interacting particle systems [See also 60K35]

Branching random walks self-catalytic branching


Birkner, Matthias; Sun, Rongfeng. Low-dimensional lonely branching random walks die out. Ann. Probab. 47 (2019), no. 2, 774--803. doi:10.1214/18-AOP1271.

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