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

IF 1.2 3区数学 Q3 MATHEMATICS, APPLIED

Mathematical Physics, Analysis and Geometry Pub Date : 2025-11-03 DOI:10.1007/s11040-025-09534-y

Taro Kimura

引用次数: 0

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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q-变形的随机分区，行列式结构，和黎曼-希尔伯特问题

我们研究了分区上概率测度的q-变形，即q-变形随机分区。我们特别考虑了q-Plancherel测度，并利用离散贝塞尔核的q-变形给出了相关函数的行列式。我们还研究了与相应正交多项式相关的Riemann-Hilbert问题，并从q-差分Lax形式中得到了q- painlev方程。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Physics, Analysis and Geometry 数学-物理：数学物理

CiteScore

2.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： MPAG is a peer-reviewed journal organized in sections. Each section is editorially independent and provides a high forum for research articles in the respective areas. The entire editorial board commits itself to combine the requirements of an accurate and fast refereeing process. The section on Probability and Statistical Physics focuses on probabilistic models and spatial stochastic processes arising in statistical physics. Examples include: interacting particle systems, non-equilibrium statistical mechanics, integrable probability, random graphs and percolation, critical phenomena and conformal theories. Applications of probability theory and statistical physics to other areas of mathematics, such as analysis (stochastic pde''s), random geometry, combinatorial aspects are also addressed. The section on Quantum Theory publishes research papers on developments in geometry, probability and analysis that are relevant to quantum theory. Topics that are covered in this section include: classical and algebraic quantum field theories, deformation and geometric quantisation, index theory, Lie algebras and Hopf algebras, non-commutative geometry, spectral theory for quantum systems, disordered quantum systems (Anderson localization, quantum diffusion), many-body quantum physics with applications to condensed matter theory, partial differential equations emerging from quantum theory, quantum lattice systems, topological phases of matter, equilibrium and non-equilibrium quantum statistical mechanics, multiscale analysis, rigorous renormalisation group.