The infinite Atlas process: Convergence to equilibrium

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.

References in corpus (2)

• Characterization of invariant measures at the leading edge for competing particle systems
• Stationary Distributions of the Atlas Model

Cited by in corpus (2)

• High moments of the SHE in the clustering regimes
• The Inert Drift Atlas Model