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Probability Distributions of Multi-species q-TAZRP and ASEP as Double Cosets of Parabolic Subgroups

  • Jeffrey KuanEmail author
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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 and Lee in J Math Phys 55:013301, 2014. arXiv:1308.4769v2, Wang and Waugh in SIGMA 12:037, 2016. arXiv:1512.01612v5) and ASEP (Tracy and Widom in Integral formulas for the asymmetric simple exclusion process, 2007. arXiv:0704.2633), 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.

Mathematics Subject Classification

Primary 05E15 Secondary 60C05 
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Authors and Affiliations

  1. 1.College StationUSA

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