A stochastic Burgers equation from a class of microscopic interactions

@article{Gonccalves2012ASB,
  title={A stochastic Burgers equation from a class of microscopic interactions},
  author={Patr'icia Gonccalves and Milton Jara and Sunder Sethuraman},
  journal={arXiv: Probability},
  year={2012}
}
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… 
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