One-dimensional random walks with self-blocking immigration
Probability
2015-09-14 v2
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 . We confirm this prediction and also describe the asymptotic macroscopic profile of the particle configuration.
Cite
@article{arxiv.1410.4344,
title = {One-dimensional random walks with self-blocking immigration},
author = {Matthias Birkner and Rongfeng Sun},
journal= {arXiv preprint arXiv:1410.4344},
year = {2015}
}
Comments
Revised version; in particular, details of the proof of the lower bound have been worked out more explicitly