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

with Herbert Spohn.

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 j=(1-2ρ)t+2w(ρ(1-ρ))^{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 Tracy-Widom 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 Riemann-Hilbert 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 space-time covariance of the stationary TASEP, equivalently to the asymptotic transition probability of a single second class particle.

Postscript file: [PS]

PDF file: [PDF]

arXiv: math-ph/0504041