A Note on Rate of Convergence in Probability to Semicircular Law
Jiang Hu (Northeast Normal University)
Guangming Pan (Nanyang Technological University)
Wang Zhou (National University of Singapore)
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.
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Pages: 2439-2451
Publication Date: November 23, 2011
DOI: 10.1214/EJP.v16-963
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