Open Access
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 ctlogt. 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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