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February 2015 A stochastic Burgers equation from a class of microscopic interactions
Patrícia Gonçalves, Milton Jara, Sunder Sethuraman
Ann. Probab. 43(1): 286-338 (February 2015). DOI: 10.1214/13-AOP878


We consider a class of nearest-neighbor weakly asymmetric mass conservative particle systems evolving on $\mathbb{Z}$, which includes zero-range and types of exclusion processes, starting from a perturbation of a stationary state. When the weak asymmetry is of order $O(n^{-\gamma})$ for $1/2<\gamma\leq1$, 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 $\gamma=1/2$, 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.


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Patrícia Gonçalves. Milton Jara. Sunder Sethuraman. "A stochastic Burgers equation from a class of microscopic interactions." Ann. Probab. 43 (1) 286 - 338, February 2015.


Published: February 2015
First available in Project Euclid: 12 November 2014

zbMATH: 1311.60069
MathSciNet: MR3298474
Digital Object Identifier: 10.1214/13-AOP878

Primary: 60K35
Secondary: 82C22

Keywords: Burgers , Fluctuations , kinetically constrained , KPZ equation , speed-change , weakly asymetric , Zero-range

Rights: Copyright © 2015 Institute of Mathematical Statistics

Vol.43 • No. 1 • February 2015
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