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Shock fluctuations in asymmetric simple exclusion
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  • Published: March 1992

Shock fluctuations in asymmetric simple exclusion

  • Pablo A. Ferrari1 

Probability Theory and Related Fields volume 91, pages 81–101 (1992)Cite this article

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Summary

The one dimensional nearest neighbors asymmetric simple exclusion process in used as a microscopic approximation to the Burgers equation. We study the process with rates of jumpsp>q to the right and left, respectively, and with initial product measure with densities ϱ<λ to the left and right of the origin, respectively (with shock initial conditions). We prove that a second class particle added to the system at the origin at time zero identifies microscopically the shock for all later times. If this particle is added at another site, then it describes the behavior of a characteristic of the Burgers equation. For vanishing left density (ϱ=0) we prove, in the scale t1/2, that the position of the shock at timet depends only on the initial configuration in a region depending ont. The proofs are based on laws of large numbers for the second class particle.

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Authors and Affiliations

  1. Instituto de Matemática e Estatistica, Universidade de São Paulo, Cx. Postal 20570, 01498 São, Paulo, Brasil

    Pablo A. Ferrari

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  1. Pablo A. Ferrari
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Ferrari, P.A. Shock fluctuations in asymmetric simple exclusion. Probab. Th. Rel. Fields 91, 81–101 (1992). https://doi.org/10.1007/BF01194491

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  • Received: 17 May 1990

  • Revised: 04 March 1991

  • Issue Date: March 1992

  • DOI: https://doi.org/10.1007/BF01194491

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