Finite-time fluctuations for the totally asymmetric exclusion process

Sylvain Prolhac

Published 2015-11-12Version 1

The one-dimensional totally asymmetric simple exclusion process (TASEP), a Markov process describing classical hard-core particles hopping in the same direction, is considered on a periodic lattice of $L$ sites. The relaxation to the non-equilibrium steady state, which occurs on the time scale $t\sim L^{3/2}$ for large $L$, is studied for the half-filled system with $N=L/2$ particles. Using large $L$ asymptotics of Bethe ansatz formulas for infinitely many eigenvalues and eigenvectors, exact expressions depending explicitly on the rescaled time $t/L^{3/2}$ are obtained for the average local density beyond Burgers' hydrodynamics, when the macroscopic shock disappears, and for the current fluctuations for simple (stationary, flat and step) initial conditions, relating previous results on the infinite line to stationary large deviations.