Shift invariance of half space integrable models

• 成果类型: Article; Early Access
• 署名作者: He, Jimmy
• 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/s00440-025-01358-9
• 发表日期: 2025
• 关键词: refined cauchy/littlewood identities; stochastic 6-vertex model; last passage percolation; current fluctuations; symmetry classes; vertex models; asep; asymptotics; particles; tasep

摘要

We formulate and establish symmetries of certain integrable half space models, analogous to recent results on symmetries for models in a full space. Our starting point is the colored stochastic six vertex model in a half space, from which we obtain results on the asymmetric simple exclusion process, as well as for the beta polymer through a fusion procedure which may be of independent interest. As an application, we establish a distributional identity between the absorption time in a type B analogue of the oriented swap process and last passage times in a half space, establishing the Baik-Ben Arous-P & eacute;ch & eacute; phase transition for the absorption time. The proof uses Hecke algebras and integrability of the six vertex model through the Yang-Baxter and reflection equations.