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August 2021 Derivation of coupled KPZ-Burgers equation from multi-species zero-range processes
C. Bernardin, T. Funaki, S. Sethuraman
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Ann. Appl. Probab. 31(4): 1966-2017 (August 2021). DOI: 10.1214/20-AAP1639


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.

Funding Statement

The work of C. Bernardin has been supported by the projects EDNHS ANR-14-CE25-0011, LSD ANR-15-CE40-0020-01 of the French National Research Agency (ANR), and funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovative programme (grant agreement No 715734). T. Funaki was supported in part by JSPS KAKENHI, Grant-in-Aid for Scientific Researches (A) 18H03672 and (S) 16H06338. S. Sethuraman was supported by grant ARO W911NF-181-0311, a Simons Foundation Sabbatical grant, and by a Japan Society for the Promotion of Science Fellowship.


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C. Bernardin. T. Funaki. S. Sethuraman. "Derivation of coupled KPZ-Burgers equation from multi-species zero-range processes." Ann. Appl. Probab. 31 (4) 1966 - 2017, August 2021.


Received: 1 November 2019; Revised: 1 July 2020; Published: August 2021
First available in Project Euclid: 15 September 2021

Digital Object Identifier: 10.1214/20-AAP1639

Primary: 60F17 , 60G60 , 60H15 , 60K35 , 82C22

Keywords: Burgers , coupled , field , Fluctuation , Interacting , KPZ , multi-species , nonlinear fluctuating hydrodynamics , Particle system , weakly asymmetric , Zero-range

Rights: Copyright © 2021 Institute of Mathematical Statistics


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Vol.31 • No. 4 • August 2021
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