Colored line ensembles for stochastic vertex models
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29_2024_989_ReferencePDF.pdf
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Author(s)
Aggarwal, Amol
Borodin, Alexei
Date Issued
November 7, 2024
Journal
Selecta Mathematica
Publisher
Springer International Publishing
Citation
Aggarwal, A., Borodin, A. Colored line ensembles for stochastic vertex models. Sel. Math. New Ser. 30, 105 (2024).
Version
Author's final manuscript
Abstract
In this paper we assign a family of n coupled line ensembles to any U q ( sl ^ n + 1 ) colored stochastic fused vertex model, which satisfies two properties. First, the joint law of their top curves coincides with that of the colored height functions for the vertex model. Second, the n line ensembles satisfy an explicit Gibbs property prescribing their laws if all but a few of their curves are conditioned upon. We further describe several examples of such families of line ensembles, including the ones for the colored stochastic six-vertex and q-boson models. The appendices (which may be of independent interest) include an explanation of how the U q ( sl ^ n + 1 ) colored stochastic fused vertex model degenerates to the log-gamma polymer, and an effective rate of convergence of the colored stochastic six-vertex model to the colored ASEP.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-ShareAlike
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DOI of Published Version
https://doi.org/10.1007/s00029-024-00989-5
