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$q$-deformed Gaussian unitary ensemble: spectral moments and genus-type expansions

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arxiv 2404.03400 v1 pith:7SZVE52F submitted 2024-04-04 math.PR math-phmath.COmath.MP

classification math.PRmath-phmath.COmath.MP
keywords momentsdensityeigenvalueensemblefunctiongaussiangenus-typeleading
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abstract

The eigenvalue probability density function of the Gaussian unitary ensemble permits a $q$-extension related to the discrete $q$-Hermite weight and corresponding $q$-orthogonal polynomials. A combinatorial counting method is used to specify a positive sum formula for the spectral moments of this model. The leading two terms of the scaled $1/N^2$ genus-type expansion of the moments are evaluated explicitly in terms of the incomplete beta function. Knowledge of these functional forms allows for the smoothed leading eigenvalue density and its first correction to be determined analytically.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Spectral analysis of $q$-deformed unitary ensembles with the Al-Salam--Carlitz weight

    math-ph 2025-07 conditional novelty 6.0 of 10

    For the q-Al-Salam-Carlitz unitary ensemble with a<0, the authors derive explicit spectral moments and a limiting density with two soft-to-hard edge phase transitions.

  2. Zeros and exponential profiles of polynomials II: Examples

    math.CA 2025-09 accept novelty 4.0 of 10

    Elaborates a companion method that converts exponential coefficient profiles into limiting zero distributions, covering Touchard, Fubini, Eulerian, Narayana, hypergeometric, q-Laguerre, free-probability, and different...

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