The infinite Atlas process: Convergence to equilibrium
Probability
2019-09-04 v2
Abstract
The semi-infinite Atlas process is a one-dimensional system of Brownian particles, where only the leftmost particle gets a unit drift to the right. Its particle spacing process has infinitely many stationary measures, with one distinguished translation invariant reversible measure. We show that the latter is attractive for a large class of initial configurations of slowly growing (or bounded) particle densities. Key to our proof is a new estimate on the rate of convergence to equilibrium for the particle spacing in a triangular array of finite, large size systems.
Cite
@article{arxiv.1709.04085,
title = {The infinite Atlas process: Convergence to equilibrium},
author = {Amir Dembo and Milton Jara and Stefano Olla},
journal= {arXiv preprint arXiv:1709.04085},
year = {2019}
}