Derivation of coupled KPZ-Burgers equation from multi-species zero-range processes

Cedric Bernardin; Tadahisa Funaki; Sunder Sethuraman

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arXiv · 1908.07863

Derivation of coupled KPZ-Burgers equation from multi-species zero-range processes

Cedric Bernardin·Tadahisa Funaki·Sunder Sethuraman

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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.

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BibTeX RIS

Cedric Bernardin, Tadahisa Funaki, Sunder Sethuraman. 2019-08-21. Derivation of coupled KPZ-Burgers equation from multi-species zero-range processes. https://arxiv.org/abs/1908.07863

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