Transition probability and total crossing events in the multi-species asymmetric exclusion process
arXiv:2109.14232 · doi:10.1088/1751-8121/acd5be
Abstract
We present explicit formulas for total crossing events in the multi-species asymmetric exclusion process (-ASEP) with underlying symmetry. In the case of the two-species TASEP these can be derived using an explicit expression for the general transition probability on in terms of a multiple contour integral derived from a nested Bethe ansatz approach. For the general -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 -TASEP, the total crossing probability can be show to reduce to a multiple integral over the product of determinants. For -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.
arXiv comment41 pages, 4 figures. Version 2 adds references and referee suggestions
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