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Convergence towards Burger's equation and propagation of chaos for weakly asymmetric exclusion processes

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  • Gärtner, Jürgen

Abstract

We consider a nearest neighbor exclusion process on with generator G[var epsilon] = Gs + [var epsilon]Ga, where Gs and Ga denote the generators of a symmetric and a totally asymmetric exclusion process, respectively. The parameter [var epsilon] characterizes the strength of asymmetry. In the limit as [var epsilon]-->0, we derive the law of large numbers for the associated "density field" in macroscopic space-time coordinates (corresponding to a space-time rescaling of the form x-->x/[var epsilon], t-->t/[var epsilon]2. The limiting deterministic dynamics is characterized as a solution of Burger's equation with viscosity. Furthermore, propagation of chaos is proven to hold in the macroscopic regime. Our approach is based on a non-linear transformation of the exclusion process which leads to a stochastic equation with a linear drift term.

Suggested Citation

  • Gärtner, Jürgen, 1987. "Convergence towards Burger's equation and propagation of chaos for weakly asymmetric exclusion processes," Stochastic Processes and their Applications, Elsevier, vol. 27, pages 233-260.
    • Handle: RePEc:eee:spapps:v:27:y:1987:i::p:233-260
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