대표연구 논문 실적
q-DEFORMED GAUSSIAN UNITARY ENSEMBLE: SPECTRAL MOMENTS AND GENUS-TYPE EXPANSIONS
발행년도
20260304
저자
SUNG-SOO BYUN, PETER J. FORRESTER, AND JAESEONG OH
저널
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
Author
전지현
Date
2026-03-17
Views
25
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/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.
http://dx.doi.org/10.1090/tran/9622
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.
http://dx.doi.org/10.1090/tran/9622
