6533b828fe1ef96bd128866b

RESEARCH PRODUCT

One-dimensional random walks with self-blocking immigration

Rongfeng SunMatthias Birkner

subject

Statistics and Probability60G50Particle numbervacant timeInteracting random walksPoisson distributionPoisson comparison01 natural sciences010104 statistics & probabilitysymbols.namesakeLattice (order)FOS: Mathematicsdensity-dependent immigrationStatistical physics0101 mathematicsAnsatzMathematics010102 general mathematicsProbability (math.PR)Random walk60K35symbolsHeat equationStatistics Probability and Uncertainty60F99Mathematics - Probability

description

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.

yearjournalcountryeditionlanguage
2017-02-01
http://arxiv.org/abs/1410.4344