Electronic Journal of Probability

Diffusion and Scattering of Shocks in the Partially Asymmetric Simple Exclusion Process

Vladimir Belitsky and Gunter Schütz

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We study the behavior of shocks in the asymmetric simple exclusion process on $Z$ whose initial distribution is a product measure with a finite number of shocks. We prove that if the particle hopping rates of this process are in a particular relation with the densities of the initial measure then the distribution of this process at any time is a linear combination of shock measures of the structure similar to that of the initial distribution. The structure of this linear combination allows us to interpret this result by saying that the shocks of the initial distribution perform continuous time random walks on $Z$ interacting by the exclusion rule. We give explicit expressions for the hopping rates of these random walks. The result is derived with a help of quantum algebra technique. We made the presentation self-contained for the benefit of readers not acquainted with this approach, but interested in applying it in the study of interacting particle systems.

Article information

Electron. J. Probab., Volume 7 (2002), paper no. 11, 21 pp.

Accepted: 21 February 2002
First available in Project Euclid: 16 May 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 82C22: Interacting particle systems [See also 60K35] 82C20: Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs 82C23: Exactly solvable dynamic models [See also 37K60]

Asymmetric simpleexclusion process evolution of shock measures quantum algebra

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Belitsky, Vladimir; Schütz, Gunter. Diffusion and Scattering of Shocks in the Partially Asymmetric Simple Exclusion Process. Electron. J. Probab. 7 (2002), paper no. 11, 21 pp. doi:10.1214/EJP.v7-110. https://projecteuclid.org/euclid.ejp/1463434884

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