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 $U_q({\widehat{\mathfrak{sl}}}_{r+1})$ symmetry. In the case of the two-species TASEP these can be derived using an explicit expression for the general transition probability on $\mathbb{Z}$ 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.

41 pages, 4 figures. Version 2 adds references and referee suggestions

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Cited by in corpus (2)

• KPZ fluctuations in finite volume
• Triangular solutions to the reflection equation for $U_q(\widehat{s{l}_n})$