Yang-Baxter field for spin Hall-Littlewood symmetric functions

2017/12/13 by Bufetov, Alexey, Petrov, Leonid
#Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Statistical Mechanics (cond-mat.stat-mech)

paper · doi:10.48550/arxiv.1712.04584

Abstract

Employing bijectivisation of summation identities, we introduce local stochastic moves based on the Yang-Baxter equation for U_q(\widehat\mathfraksl₂). Combining these moves leads to a new object which we call the spin Hall-Littlewood Yang-Baxter field - a probability distribution on two-dimensional arrays of particle configurations on the discrete line. We identify joint distributions along down-right paths in the Yang-Baxter field with spin Hall-Littlewood processes, a generalization of Schur processes. We consider various degenerations of the Yang-Baxter field leading to new dynamic versions of the stochastic six vertex model and of the Asymmetric Simple Exclusion Process.

Related

• Stable spin Hall-Littlewood symmetric functions, combinatorial identities, and half-space Yang-Baxter random field
• Yang-Baxter random fields and stochastic vertex models
• Hall-Littlewood RSK field
• Lectures on Integrable probability: Stochastic vertex models and symmetric functions
• Refined Cauchy identity for spin Hall-Littlewood symmetric rational\n functions