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Local semicircle law under weak moment conditions (2016)

Springer

In: Doklady Mathematics

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Publication Date: 2016-07-17

Description: Symmetric random matrices are considered whose upper triangular entries are independent identically distributed random variables with zero mean, unit variance, and a finite moment of order 4 + δ, δ 〉 0. It is shown that the distances between the Stieltjes transforms of the empirical spectral distribution function and the semicircle law are of order ln n / nv , where v is the distance to the real axis in the complex plane. Applications concerning the convergence rate in probability to the semicircle law, localization of eigenvalues, and delocalization of eigenvectors are discussed.

Print ISSN: 1064-5624

Electronic ISSN: 1531-8362

Topics: Mathematics

Published by Springer

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