Equilibrium Fluctuations for a Discrete Atlas Model
Probability
2015-07-20 v1 Statistical Mechanics
Abstract
We consider a discrete version of the Atlas model, which corresponds to a sequence of zero-range processes on a semi-infinite line, with a source at the origin and a diverging density of particles. We show that the equilibrium fluctuations of this model are governed by a stochastic heat equation with Neumann boundary conditions. As a consequence, we show that the current of particles at the origin converges to a fractional Brownian motion of Hurst exponent H=1/4.
Cite
@article{arxiv.1507.04786,
title = {Equilibrium Fluctuations for a Discrete Atlas Model},
author = {F. Hernández and M. Jara and Fabio J. Valentim},
journal= {arXiv preprint arXiv:1507.04786},
year = {2015}
}
Comments
17 pages