 05134 Patrik L. Ferrari, Herbert Spohn
 Scaling Limit for the SpaceTime Covariance of the Stationary Totally Asymmetric Simple Exclusion Process
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Apr 13, 05

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Abstract. The totally asymmetric simple exclusion process (TASEP) on the onedimensional lattice with the Bernoulli \rho measure as initial conditions, 0<\rho<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 j=(12\rho)t+2w(\rho(1\rho))^{1/3} t^{2/3} we prove that the fluctuations of N_t(j) for large t are of order t^{1/3} and we determine the limiting distribution function F_w(s), which is a generalization of the GUE TracyWidom distribution. The family F_w(s) 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 RiemannHilbert problem. In our work we arrive at F_w(s) through the asymptotics of a Fredholm determinant. F_w(s) is simply related to the scaling function for the spacetime covariance of the stationary TASEP, equivalently to the asymptotic transition probability of a single second class particle.
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