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February 2017 One-dimensional random walks with self-blocking immigration
Matthias Birkner, Rongfeng Sun
Ann. Appl. Probab. 27(1): 109-139 (February 2017). DOI: 10.1214/16-AAP1199

Abstract

We consider a system of independent one-dimensional random walkers where new particles are added at the origin at fixed rate whenever there is no older particle present at the origin. A Poisson ansatz leads to a semi-linear lattice heat equation and predicts that starting from the empty configuration the total number of particles grows as $c\sqrt{t}\log t$. We confirm this prediction and also describe the asymptotic macroscopic profile of the particle configuration.

Citation

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Matthias Birkner. Rongfeng Sun. "One-dimensional random walks with self-blocking immigration." Ann. Appl. Probab. 27 (1) 109 - 139, February 2017. https://doi.org/10.1214/16-AAP1199

Information

Received: 1 October 2014; Revised: 1 September 2015; Published: February 2017
First available in Project Euclid: 6 March 2017

zbMATH: 1362.60082
MathSciNet: MR3619784
Digital Object Identifier: 10.1214/16-AAP1199

Subjects:
Primary: 60K35
Secondary: 60F99 , 60G50

Keywords: density-dependent immigration , Interacting random walks , Poisson comparison , vacant time

Rights: Copyright © 2017 Institute of Mathematical Statistics

Vol.27 • No. 1 • February 2017
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