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arXiv · 1709.04085

The infinite Atlas process: Convergence to equilibrium

Amir Dembo·Milton Jara·Stefano Olla
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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.

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Amir Dembo, Milton Jara, Stefano Olla. 2017-09-12. The infinite Atlas process: Convergence to equilibrium. https://doi.org/10.1214/17-aihp875

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