The Polynomial Method for Random Matrices

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N. Raj Rao, Alan Edelman

Published: 2008, Last Modified: 12 May 2025Found. Comput. Math. 2008EveryoneRevisionsBibTeXCC BY-SA 4.0
Abstract: We define a class of “algebraic” random matrices. These are random matrices for which the Stieltjes transform of the limiting eigenvalue distribution function is algebraic, i.e., it satisfies a (bivariate) polynomial equation. The Wigner and Wishart matrices whose limiting eigenvalue distributions are given by the semicircle law and the Marčenko–Pastur law are special cases.