Universal exit probabilities in the TASEP

Abstract

We study the joint exit probabilities of particles in the totally asymmetric simple exclusion process (TASEP) from space-time sets of given form. We extend previous results on the space-time correlation functions of the TASEP, which correspond to exits from the sets bounded by straight vertical or horizontal lines. In particular, our approach allows us to remove ordering of time moments used in previous studies so that only a natural space-like ordering of particle coordinates remains. We consider sequences of general staircase-like boundaries going from the northeast to southwest in the space-time plane. The exit probabilities from the given sets are derived in the form of Fredholm determinant defined on the boundaries of the sets. In the scaling limit, the staircase-like boundaries are treated as approximations of continuous differentiable curves. The exit probabilities with respect to points of these curves belonging to arbitrary space-like path are shown to converge to the universal Airy${}_2$ process.

46 pages, 7 figures

References in corpus (6)

• Exact scaling functions for one-dimensional stationary KPZ growth
• Fluctuation properties of the TASEP with periodic initial configuration
• Transition between Airy_1 and Airy_2 processes and TASEP fluctuations
• Current Distribution and random matrix ensembles for an integrable asymmetric fragmentation process
• Dynamics of a tagged particle in the asymmetric exclusion process with the step initial condition
• Slow decorrelations in KPZ growth