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July 2021 Color-position symmetry in interacting particle systems
Alexei Borodin, Alexey Bufetov
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Ann. Probab. 49(4): 1607-1632 (July 2021). DOI: 10.1214/20-AOP1463

Abstract

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.

Funding Statement

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.”

Acknowledgments

We are grateful to A. Aggarwal and P. L. Ferrari for very valuable comments.

Citation

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Alexei Borodin. Alexey Bufetov. "Color-position symmetry in interacting particle systems." Ann. Probab. 49 (4) 1607 - 1632, July 2021. https://doi.org/10.1214/20-AOP1463

Information

Received: 1 June 2019; Revised: 1 May 2020; Published: July 2021
First available in Project Euclid: 13 May 2021

Digital Object Identifier: 10.1214/20-AOP1463

Subjects:
Primary: 60K35

Rights: Copyright © 2021 Institute of Mathematical Statistics

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Vol.49 • No. 4 • July 2021
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