A stochastic burgers equation from a class of microscopic interactions

Patrícia Gonçalves, Milton Jara, Sunder Sethuraman

Research output: Contribution to journalArticle

20 Scopus citations

Abstract

We consider a class of nearest-neighbor weakly asymmetric mass conservative particle systems evolving on Z, which includes zero-range and types of exclusion processes, starting from a perturbation of a stationary state. When the weak asymmetry is of order O(n ) for 1/2 < γ ≤ 1, we show that the scaling limit of the fluctuation field, as seen across process characteristics, is a generalized Ornstein-Uhlenbeck process. However, at the critical weak asymmetry when γ = 1/2, we show that all limit points satisfy a martingale formulation which may be interpreted in terms of a stochastic Burgers equation derived from taking the gradient of the KPZ equation. The proofs make use of a sharp "Boltzmann-Gibbs" estimate which improves on earlier bounds.

Original languageEnglish (US)
Pages (from-to)286-338
Number of pages53
JournalAnnals of Probability
Volume43
Issue number1
DOIs
StatePublished - Jan 1 2015

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Keywords

  • Burgers
  • Fluctuations
  • KPZ equation
  • Kinetically constrained
  • Speed-change
  • Weakly asymetric
  • Zero-range

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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