Stationary stochastic Higher Spin Six Vertex Model and q-Whittaker measure

• 成果类型: Article
• 署名作者: Imamura, Takashi; Mucciconi, Matteo; Sasamoto, Tomohiro
• 署名单位: Chiba University; Institute of Science Tokyo; Tokyo Institute of Technology
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-020-00966-x
• 发表日期: 2020
• 页码: 923-1042
• 关键词: current fluctuations; kpz equation; growth-model; distributions; tasep; limit; asymptotics; geometry; Duality; polymer

摘要

In this paper we consider the Higher Spin Six Vertex Model on the lattice Z >= 2xZ >= 1. We first identify a family of translation invariant measures and subsequently we study the one point distribution of the height function for the model with certain random boundary conditions. Exact formulas we obtain prove to be useful in order to establish the asymptotic of the height distribution in the long space-time limit for the stationary Higher Spin Six Vertex Model. In particular, along the characteristic line we recover Baik-Rains fluctuations with size of characteristic exponent 1/3. We also consider some of the main degenerations of the Higher Spin Six Vertex Model and we adapt our analysis to the relevant cases of the q-Hahn particle process and of the Exponential Jump Model.