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Scaling Limit for the Space-Time Covariance of the Stationary Totally Asymmetric Simple Exclusion Process

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A Publisher's Erratum to this article was published on 29 April 2006

Abstract

The totally asymmetric simple exclusion process (TASEP) on the one-dimensional lattice with the Bernoulli ρ measure as initial conditions, 0<ρ<1, is stationary in space and time. Let N t (j) be the number of particles which have crossed the bond from j to j+1 during the time span [0,t]. For we prove that the fluctuations of N t (j) for large t are of order t1/3 and we determine the limiting distribution function , which is a generalization of the GUE Tracy-Widom distribution. The family of distribution functions have been obtained before by Baik and Rains in the context of the PNG model with boundary sources, which requires the asymptotics of a Riemann-Hilbert problem. In our work we arrive at through the asymptotics of a Fredholm determinant. is simply related to the scaling function for the space-time covariance of the stationary TASEP, equivalently to the asymptotic transition probability of a single second class particle.

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Authors and Affiliations

  1. Zentrum Mathematik and Physik Department, Technische Universität München, Boltzmannstr. 3, 85747, Garching, Germany

    Patrik L. Ferrari & Herbert Spohn

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  1. Patrik L. Ferrari
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  2. Herbert Spohn
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Correspondence to Patrik L. Ferrari.

Additional information

Communicated by M. Aizenman

An erratum to this article can be found at http://dx.doi.org/10.1007/s00220-006-1559-y

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Ferrari, P., Spohn, H. Scaling Limit for the Space-Time Covariance of the Stationary Totally Asymmetric Simple Exclusion Process. Commun. Math. Phys. 265, 1–44 (2006). https://doi.org/10.1007/s00220-006-1549-0

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  • DOI: https://doi.org/10.1007/s00220-006-1549-0

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