Periodic q-Whittaker and Hall–Littlewood processes

• Jimmy He ^[1] ; Michael Wheeler ^[2]
  1. [1] Ohio State University

     Ohio State University

     City of Columbus, Estados Unidos

     
  2. [2] University of Melbourne,Australia
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 32, Nº. 1, 2026
• Idioma: inglés
• DOI: 10.1007/s00029-025-01113-x
• Enlaces
  • Texto completo
• Resumen

  • 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.

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