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

C. Bernardin, T. Funaki, S. Sethuraman

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)1966-2017
Number of pages52
JournalAnnals of Applied Probability
Volume31
Issue number4
DOIs
StatePublished - Aug 2021

Keywords

  • Burgers
  • Coupled
  • Field
  • Fluctuation
  • Interacting
  • KPZ
  • Multi-species
  • Nonlinear fluctuating hydrodynamics
  • Particle system
  • Weakly asymmetric
  • Zero-range

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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