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March 2019 Low-dimensional lonely branching random walks die out
Matthias Birkner, Rongfeng Sun
Ann. Probab. 47(2): 774-803 (March 2019). DOI: 10.1214/18-AOP1271

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.

Citation

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Matthias Birkner. Rongfeng Sun. "Low-dimensional lonely branching random walks die out." Ann. Probab. 47 (2) 774 - 803, March 2019. https://doi.org/10.1214/18-AOP1271

Information

Received: 1 August 2017; Revised: 1 March 2018; Published: March 2019
First available in Project Euclid: 26 February 2019

zbMATH: 07053556
MathSciNet: MR3916934
Digital Object Identifier: 10.1214/18-AOP1271

Subjects:
Primary: 60K35
Secondary: 82C22

Rights: Copyright © 2019 Institute of Mathematical Statistics

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Vol.47 • No. 2 • March 2019
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