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Central limit theorem for a tagged particle in asymmetric simple exclusion

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  • Gonçalves, Patrícia

Abstract

We prove a functional central limit theorem for the position of a tagged particle in the one-dimensional asymmetric simple exclusion process for hyperbolic scaling, starting from a Bernoulli product measure conditioned to have a particle at the origin. We also prove that the position of the tagged particle at time t depends on the initial configuration, through the number of empty sites in the interval [0,(p-q)[alpha]t] divided by [alpha], on the hyperbolic time scale and on a longer time scale, namely N4/3.

Suggested Citation

  • Gonçalves, Patrícia, 2008. "Central limit theorem for a tagged particle in asymmetric simple exclusion," Stochastic Processes and their Applications, Elsevier, vol. 118(3), pages 474-502, March.
    • Handle: RePEc:eee:spapps:v:118:y:2008:i:3:p:474-502
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    References listed on IDEAS

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    1. Assing, Sigurd, 2007. "A limit theorem for quadratic fluctuations in symmetric simple exclusion," Stochastic Processes and their Applications, Elsevier, vol. 117(6), pages 766-790, June.
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    Cited by:

    1. Franco, Tertuliano & Gonçalves, Patrícia & Neumann, Adriana, 2013. "Phase transition in equilibrium fluctuations of symmetric slowed exclusion," Stochastic Processes and their Applications, Elsevier, vol. 123(12), pages 4156-4185.

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