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Shock fluctuations in the asymmetric simple exclusion process
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  • Published: June 1994

Shock fluctuations in the asymmetric simple exclusion process

  • P. A. Ferrari1 &
  • L. R. G. Fontes1 

Probability Theory and Related Fields volume 99, pages 305–319 (1994)Cite this article

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Summary

We consider the one dimensional nearest neighbors asymmetric simple exclusion process with ratesq andp for left and right jumps respectively;q<p. Ferrari et al. (1991) have shown that if the initial measure isv ρ,λ , a product measure with densities ρ and λ to the left and right of the origin respectively, ρ<λ, then there exists a (microscopic) shock for the system. A shock is a random positionX t such that the system as seen from this position at timet has asymptotic product distributions with densities ρ and λ to the left and right of the origin respectively, uniformly int. We compute the diffusion coefficient of the shockD=lim t→∞ t −1(E(X t )2−(EX t )2) and findD=(p−q)(λ−ρ)−1(ρ(1−ρ)+λ(1−λ)) as conjectured by Spohn (1991). We show that in the scale\(\sqrt t\) the position ofX t is determined by the initial distribution of particles in a region of length proportional tot. We prove that the distribution of the process at the average position of the shock converges to a fair mixture of the product measures with densities ρ and λ. This is the so called dynamical phase transition. Under shock initial conditions we show how the density fluctuation fields depend on the initial configuration.

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Authors and Affiliations

  1. Instituto de Matemática e Estatística, Universidade de São Paulo, Cx. Postal 20570, 01452-010, São Paulo, SP, Brasil

    P. A. Ferrari & L. R. G. Fontes

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  1. P. A. Ferrari
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  2. L. R. G. Fontes
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Ferrari, P.A., Fontes, L.R.G. Shock fluctuations in the asymmetric simple exclusion process. Probab. Th. Rel. Fields 99, 305–319 (1994). https://doi.org/10.1007/BF01199027

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  • Received: 19 February 1993

  • Revised: 11 November 1993

  • Issue Date: June 1994

  • DOI: https://doi.org/10.1007/BF01199027

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Mathematics Subject Classification 1991

  • 60K35
  • 82C22
  • 82C24
  • 82C41
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