2023/10/05 by Jimmy He, Michael Wheeler, He, Jimmy +1 · 1 citation
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Bayesian Methods and Mixture Models #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Random Matrices and Applications
paper · pdf · doi:10.48550/arxiv.2310.03527
openalex publication_date 2023/10/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the periodic q-Whittaker and Hall-Littlewood processes, two probability measures on sequences of partitions. We prove that a certain observable of the periodic q-Whittaker process exhibits a (q,u) symmetry after a random shift, generalizing a previous result of Imamura, Mucciconi, and Sasamoto who showed a matching between the periodic Schur and q-Whittaker measures, and also give a vertex model formulation of their result. As part of our proof of the (q,u) symmetry, we obtain contour integral formulas for both the periodic q-Whittaker and Hall-Littlewood processes. We also show a matching between certain observables in the periodic Hall-Littlewood process and in a quasi-periodic stochastic six vertex model after a suitable random shift, and discuss a limit to the stationary periodic stochastic six vertex model.