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

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.

References in corpus (1)

• The Transition Probability of the $q$-TAZRP ($q$-Bosons) with Inhomogeneous Jump Rates

Cited by in corpus (4)

• Switching interacting particle systems: scaling limits, uphill diffusion and boundary layer
• Limiting current distribution for a two species asymmetric exclusion process
• KPZ fluctuations in finite volume
• Transition probability and total crossing events in the multi-species asymmetric exclusion process