$q$-deformation of random partitions, determinantal structure, and Riemann-Hilbert problem
Combinatorics
2025-12-09 v2 Mathematical Physics
math.MP
Probability
Abstract
We study -deformation of probability measures on partitions, i.e., -deformed random partitions. We in particular consider the -Plancherel measure and show a determinantal formula for the correlation function using a -deformation of the discrete Bessel kernel. We also investigate Riemann-Hilbert problems associated with the corresponding orthogonal polynomials and obtain -Painlev\'{e} equations from the -difference Lax formalism.
Keywords
Cite
@article{arxiv.2503.00766,
title = {$q$-deformation of random partitions, determinantal structure, and Riemann-Hilbert problem},
author = {Taro Kimura},
journal= {arXiv preprint arXiv:2503.00766},
year = {2025}
}
Comments
26 pages, v2. published version, presentation improved, references added