2024/04/04 by Sung‐Soo Byun, Peter J. Forrester, Byun, Sung-Soo +3 · 2 citations
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Mathematical functions and polynomials #Probability (math.PR) #Random Matrices and Applications
paper · pdf · doi:10.48550/arxiv.2404.03400
openalex publication_date 2024/04/04 · openalex created_date 2024/04/06 · openalex updated_date 2026/07/28
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/N2 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.