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arXiv · 1801.02313

Probability distributions of multi-species q-TAZRP and ASEP as double cosets of parabolic subgroups

Jeffrey Kuan
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Abstract

We write explicit contour integral formulas for probability distributions of the multi-species q-TAZRP and the multi-species ASEP starting with q-exchangeable initial conditions. The formulas are equal to the corresponding explicit contour integral formulas for the single-species q-TAZRP ([Korhonen-Lee 2014, Wang-Waugh 2016]) and ASEP [Tracy-Widom 2007], with a factor in front of the integral. For the multi-species q-TAZRP, we use a decomposition theorem for elements of double cosets of parabolic subgroups in a Coxeter group. The set of distinguished double coset representatives with minimal length is viewed as a particle configuration. For the multi-species ASEP we use a more direct proof.

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Jeffrey Kuan. 2018-01-08. Probability distributions of multi-species q-TAZRP and ASEP as double cosets of parabolic subgroups. https://doi.org/10.1007/s00023-019-00761-y

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