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Travelling waves and long-time behaviour of the weakly asymmetric exclusion process
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  • Published: December 1990

Travelling waves and long-time behaviour of the weakly asymmetric exclusion process

  • Peter Dittrich1 

Probability Theory and Related Fields volume 86, pages 443–455 (1990)Cite this article

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Summary

We consider the one-dimensional weakly asymmetric nearest neighbour exclusion process and study its macroscopic behaviour on a longer time scale than that for which the deterministic approximation by the Burgers equation holds. We show that this long-time behaviour is completely determined by the initial particle configuration, and does not depend on the randomness of the evolution. Moreover, we examine in detail a special case for which a travelling wave is observed with stable profile but randomly fluctuating space location.

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Authors and Affiliations

  1. Karl-Weierstrass Institute of Mathematics, Academy of Sciences, Mohrenstrasse 39, DDR-1086, Berlin, German Democratic Republic

    Peter Dittrich

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  1. Peter Dittrich
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Dittrich, P. Travelling waves and long-time behaviour of the weakly asymmetric exclusion process. Probab. Th. Rel. Fields 86, 443–455 (1990). https://doi.org/10.1007/BF01198168

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  • Received: 12 July 1989

  • Revised: 09 March 1990

  • Issue Date: December 1990

  • DOI: https://doi.org/10.1007/BF01198168

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Keywords

  • Stochastic Process
  • Probability Theory
  • Mathematical Biology
  • Burger Equation
  • Initial Particle
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