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<p>We study <i>q</i>-deformation of probability measures on partitions, i.e., <i>q</i>-deformed random partitions. We in particular consider the <i>q</i>-Plancherel measure and show a determinantal formula for the correlation function using a <i>q</i>-deformation of the discrete Bessel kernel. We also investigate Riemann–Hilbert problems associated with the corresponding orthogonal polynomials and obtain <i>q</i>-Painlevé equations from the <i>q</i>-difference Lax formalism.</p>

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q-deformation of random partitions, determinantal structure, and Riemann–Hilbert problem

  • 期刊论文

  • 发表日期：

    2025年11月3日

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  • Taro Kimura

摘要

We study q-deformation of probability measures on partitions, i.e., q-deformed random partitions. We in particular consider the q-Plancherel measure and show a determinantal formula for the correlation function using a q-deformation of the discrete Bessel kernel. We also investigate Riemann–Hilbert problems associated with the corresponding orthogonal polynomials and obtain q-Painlevé equations from the q-difference Lax formalism.