Scholarlink

<p>We study the periodic <i>q</i>-Whittaker and Hall–Littlewood processes, two probability measures on sequences of partitions. We prove that a certain observable of the periodic <i>q</i>-Whittaker process exhibits a (<i>q</i>,&#xa0;<i>u</i>) symmetry after a random shift, generalizing a previous result of Imamura, Mucciconi, and Sasamoto who showed a matching between the periodic Schur and <i>q</i>-Whittaker measures, and also give a vertex model formulation of their result. As part of our proof of the (<i>q</i>,&#xa0;<i>u</i>) symmetry, we obtain contour integral formulas for both the periodic <i>q</i>-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.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Periodic q-Whittaker and Hall–Littlewood processes

  • 期刊论文

  • 发表日期：

    2026年1月5日

查看全文
  • Jimmy He,
  • Michael Wheeler

摘要

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.