We prove a color-position symmetry for a class of ASEP-like interacting particle systems with discrete time on the one-dimensional lattice. The full space-time inhomogeneity of our systems allows to apply the result to colored (or multi-species) ASEP and stochastic vertex models for a certain class of initial/boundary conditions, generalizing previous results of Amir–Angel–Valko and Borodin–Wheeler. We are also able to use the symmetry, together with previously known results for uncolored models, to find novel asymptotic behavior of the second-class particles in several situations.
The work of A. Borodin was partially supported by the NSF Grants DMS-1607901 and DMS-1664619. The work of A. Bufetov was partially supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy—EXC 2047 “Hausdorff Center for Mathematics.”
We are grateful to A. Aggarwal and P. L. Ferrari for very valuable comments.
"Color-position symmetry in interacting particle systems." Ann. Probab. 49 (4) 1607 - 1632, July 2021. https://doi.org/10.1214/20-AOP1463