Hidden diagonal integrability of q-Hahn vertex model and Beta polymer model

• 成果类型: Article
• 署名作者: Korotkikh, Sergei
• 署名单位: Massachusetts Institute of Technology (MIT)
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-022-01117-0
• 发表日期: 2022
• 页码: 493-570
• 关键词: tracy-widom asymptotics; free-energy

摘要

We study a new integrable probabilistic system, defined in terms of a stochastic colored vertex model on a square lattice. The main distinctive feature of our model is a new family of parameters attached to diagonals rather than to rows or columns, like in other similar models. Because of these new parameters the previously known results about vertex models cannot be directly applied, but nevertheless the integrability remains, and we prove explicit integral expressions for q-deformed moments of the (colored) height functions of the model. Following known techniques our model can be interpreted as a q-discretization of the Beta polymer model from (Probab Theory Relat Fields 167(3):1057-1116 (2017). ) with a new family of parameters, also attached to diagonals. To demonstrate how integrability with respect to the new diagonal parameters works, we extend the known results about Tracy-Widom large-scale fluctuations of the Beta polymer model.