### 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^{-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.

Original language | English (US) |
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Pages (from-to) | 286-338 |

Number of pages | 53 |

Journal | Annals of Probability |

Volume | 43 |

Issue number | 1 |

DOIs | |

State | Published - 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

### Cite this

*Annals of Probability*,

*43*(1), 286-338. https://doi.org/10.1214/13-AOP878