Derivation of coupled KPZ-Burgers equation from multi-species zero-range processes
Probability
2019-08-22 v1 Statistical Mechanics
Mathematical Physics
math.MP
Abstract
We consider the fluctuation fields of multi-species weakly-asymmetric zero-range interacting particle systems in one dimension, where the mass density of each species is conserved. Although such fields have been studied in systems with a single species, the multi-species setting is much less understood. Among other results, we show that, when the system starts from stationary states, with a particular property, the scaling limits of the multi-species fluctuation fields, seen in a characteristic traveling frame, solve a coupled Burgers SPDE, which is a formal spatial gradient of a coupled KPZ equation.
Keywords
Cite
@article{arxiv.1908.07863,
title = {Derivation of coupled KPZ-Burgers equation from multi-species zero-range processes},
author = {Cedric Bernardin and Tadahisa Funaki and Sunder Sethuraman},
journal= {arXiv preprint arXiv:1908.07863},
year = {2019}
}