This paper is a follow-up of the work initiated in \cite{CDGP1}, where we investigated the hydrodynamic limit of symmetric independent random walkers with birth at the origin and death at the rightmost occupied site. Here we obtain two further results: first we characterize the stationary states on the hydrodynamic time scale as a family of linear macroscopic profiles parameterized by their mass. Then we prove that beyond hydrodynamics there exists a longer time scale where the evolution becomes random. On such a super-hydrodynamic scale the particle system is at each time close to the stationary state with same mass and the mass fluctuates performing a Brownian motion reflected at the origin.

Super-hydrodynamic limit in interacting particle systems

DE MASI, Anna;
2014

Abstract

This paper is a follow-up of the work initiated in \cite{CDGP1}, where we investigated the hydrodynamic limit of symmetric independent random walkers with birth at the origin and death at the rightmost occupied site. Here we obtain two further results: first we characterize the stationary states on the hydrodynamic time scale as a family of linear macroscopic profiles parameterized by their mass. Then we prove that beyond hydrodynamics there exists a longer time scale where the evolution becomes random. On such a super-hydrodynamic scale the particle system is at each time close to the stationary state with same mass and the mass fluctuates performing a Brownian motion reflected at the origin.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11697/1009
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