One-dimensional random walks with self-blocking immigration

2014/10/16 by Matthias Birkner, Birkner, Matthias, Rongfeng Sun +1
Mathematics · #FOS: Mathematics #Probability (math.PR) #math.PR

paper · pdf · doi:10.48550/arxiv.1410.4344

Revised version; in particular, details of the proof of the lower bound have been worked out more explicitly

arxiv created 2015/09/11 · arxiv updated 2015/09/14

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 √(t) log t. We confirm this prediction and also describe the asymptotic macroscopic profile of the particle configuration.

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