Transition probability and total crossing events in the multi-species asymmetric exclusion process

Abstract

We present explicit formulas for total crossing events in the multi-species asymmetric exclusion process (r-ASEP) with underlying Uq( slr+1) symmetry. In the case of the two-species TASEP these can be derived using an explicit expression for the general transition probability on Z in terms of a multiple contour integral derived from a nested Bethe ansatz approach. For the general r-ASEP we employ a vertex model approach within which the probability of total crossing can be derived from partial symmetrization of an explicit high rank rainbow partition function. In the case of r-TASEP, the total crossing probability can be show to reduce to a multiple integral over the product of r determinants. For 2-TASEP we additionally derive convenient formulas for cumulative total crossing probabilities using Bernoulli-step initial conditions for particles of type 2 and type 1 respectively.

Riemann surfaces for KPZ with periodic boundaries

“…[545,[567][568][569]. Exact integral formulas were obtained for time-dependent microscopic probabilities [570][571][572][573][574], and GUE Tracy-Widom distributions were found for current fluctuations [575,576], in agreement with the predictions [577] from non-linear fluctuating hydrodynamics for the KPZ modes. for TASEP with two types of particles corresponding to the configuration of the system shown at the bottom.…”