%0 Journal Article
%T One-dimensional random walks with self-blocking immigration
%A Matthias Birkner
%A Rongfeng Sun
%J Mathematics
%D 2014
%I arXiv
%X 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.
%U http://arxiv.org/abs/1410.4344v2