M. Bouali, M. S. Hamouda, Hind K. Al Jeaid, “Zeros of Generalized Hermite Polynomials and Ensemble of Gaussian Random Matrices”, Mat. Zametki, 2022, Volume 112, Issue 1,Pages <nobr>40

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Papers published in the English version of the journal

Zeros of Generalized Hermite Polynomials and Ensemble of Gaussian Random Matrices

M. Bouali^a, M. S. Hamouda^a, Hind K. Al Jeaid^b

^a Department of Mathematics, Institute Preparatory of Engineering of Tunis, Montfleury, 1089 Tunisia
^b Department of Applied Mathematics, College of Applied Sciences, Umm Al Qura University, Makkah, 24382 Saudi Arabia

Abstract: The main purpose of the present paper is to investigate the global asymptotic eigenvalue density of the fixed-trace generalized Gaussian ensemble of random matrices. To answer such a question, we begin with a complete study of the zeros of generalized Hermite orthogonal polynomials which are closely related to the eigenvalues in question.

Keywords: orthogonal polynomials, probability measures, logarithmic potential.

Received: 05.02.2019
Revised: 11.10.2021

Language: English