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arXiv · 2503.00766

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

Taro Kimura
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Abstract

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.

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Taro Kimura. 2025-10-18. $q$-deformation of random partitions, determinantal structure, and Riemann-Hilbert problem. https://doi.org/10.1007/s11040-025-09534-y

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