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A stochastic Burgers equation from a class of microscopic interactions | | Patricia Goncalves
; Milton Jara
; Sunder Sethuraman
; | | Date: |
28 Sep 2012 | | Abstract: | 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 $1/2<gammaleq 1$, 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 $gamma = 1/2$, we show that all limit points
solve a martingale problem 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. | | Source: | arXiv, 1210.0017 | | Services: | Forum | Review | PDF | Favorites | |
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