## The Annals of Applied Probability

### One-dimensional random walks with self-blocking immigration

#### 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.

#### Article information

Source
Ann. Appl. Probab. Volume 27, Number 1 (2017), 109-139.

Dates
Revised: September 2015
First available in Project Euclid: 6 March 2017

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1488790824

Digital Object Identifier
doi:10.1214/16-AAP1199

Mathematical Reviews number (MathSciNet)
MR3619784

Zentralblatt MATH identifier
1362.60082

#### Citation

Birkner, Matthias; Sun, Rongfeng. One-dimensional random walks with self-blocking immigration. Ann. Appl. Probab. 27 (2017), no. 1, 109--139. doi:10.1214/16-AAP1199. https://projecteuclid.org/euclid.aoap/1488790824

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