Scaling Limit for the Space-Time Covariance of the Stationary Totally Asymmetric Simple Exclusion Process |
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Authors: | Patrik L Ferrari Herbert Spohn |
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Institution: | 1. Zentrum Mathematik and Physik Department, Technische Universit?t München, Boltzmannstr. 3, 85747, Garching, Germany
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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 Nt(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 Nt(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.
An erratum to this article can be found at |
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