A stochastic Burgers equation from a class of microscopic interactions

• Gonçalves, Patrícia ^[1] ; Jara, Milton ^[1] ; Sethuraman, Sunder ^[2]
  1. [1] Universidade do Minho

     Universidade do Minho

     Braga (São José de São Lázaro), Portugal

     
  2. [2] University of Arizona

     University of Arizona

     Estados Unidos

     
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 43, Nº. 1, 2015, págs. 286-338
• Idioma: inglés
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• Resumen

  • 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−γ) 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.