SuperHydrodynamic Limit in Interacting Particle Systems
Abstract
This paper is a followup of the work initiated in (Arab J Math, 2014), 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 superhydrodynamic 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.
 Publication:

Journal of Statistical Physics
 Pub Date:
 June 2014
 DOI:
 10.1007/s1095501409840
 arXiv:
 arXiv:1312.0640
 Bibcode:
 2014JSP...155..867C
 Keywords:

 Mathematics  Probability;
 Condensed Matter  Statistical Mechanics;
 Mathematical Physics
 EPrint:
 22 pages