2022/05/25 by Jimmy He, He, Jimmy
Mathematics · #60K35 #82C22(Secondary) #82C23 (Primary) #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph) #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2205.13029
openalex publication_date 2022/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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--Péché 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.