Yang-Baxter random fields and stochastic vertex models
Abstract
Bijectivization refines the Yang-Baxter equation into a pair of local Markov moves which randomly update the configuration of the vertex model. Employing this approach, we introduce new Yang-Baxter random fields of Young diagrams based on spin -Whittaker and spin Hall-Littlewood symmetric functions. We match certain scalar Markovian marginals of these fields with (1) the stochastic six vertex model; (2) the stochastic higher spin six vertex model; and (3) a new vertex model with pushing which generalizes the -Hahn PushTASEP introduced recently by Corwin-Matveev-Petrov (arXiv:1811.06475). Our matchings include models with two-sided stationary initial data, and we obtain Fredholm determinantal expressions for the -Laplace transforms of the height functions of all these models. Moreover, we also discover difference operators acting diagonally on spin -Whittaker or (stable) spin Hall-Littlewood symmetric functions.
Cite
@article{arxiv.1905.06815,
title = {Yang-Baxter random fields and stochastic vertex models},
author = {Alexey Bufetov and Matteo Mucciconi and Leonid Petrov},
journal= {arXiv preprint arXiv:1905.06815},
year = {2019}
}
Comments
77 pages, 25 figures; v2: minor improvements of the presentation