A Note on Rate of Convergence in Probability to Semicircular Law

Zhidong Bai, Jiang Hu, Guangming Pan, Zhou Wang

Type: Article

Publication Date: 2011-01-01

Citations: 14

DOI: https://doi.org/10.1214/ejp.v16-963

Abstract

In the present paper, we prove that under the assumption of the finite sixth moment for elements of a Wigner matrix, the convergence rate of its empirical spectral distribution to the Wigner semicircular law in probability is $O(n^{-1/2})$ when the dimension n tends to infinity.

Locations

Electronic Journal of Probability - View - PDF
arXiv (Cornell University) - View - PDF

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