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A Central Limit Theorem for the Weakly Asymmetric Simple Exclusion Process

✍ Scribed by Peter Dittrich; Jürgen Gärtner

Publisher
John Wiley and Sons
Year
1991
Tongue
English
Weight
661 KB
Volume
151
Category
Article
ISSN
0025-584X

No coin nor oath required. For personal study only.

✦ Synopsis

We consider tlie one-dimensional weakly asymmetric nearest nrighbour excliision procvss and study, in macrosropic space-time coordinates, the fluctuations of tlie associated density field around tlie solution of the nonlinear BURGERS equation with viscosity. We show that this fluctuations convrrgr to ti generalized ORNSTEIN-UHLENBECK process, the drift term of nliicli can be obtaincd by linearization of the BURGERS equation. Our approach is based on ti nonlinear transformation of the exclusion process.

I. Introdoction

Stutlyirig the time evolution of stochastic particle systems one is often interested in macroscopic properties which shoriltl he determined by some cleterministic equation.

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