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• W2037413976 abstract "The universality for the eigenvalue spacing statistics of generalized Wigner matrices was established in our previous work cite{EYY} under certain conditions on the probability distributions of the matrix elements. A major class of probability measures excluded in cite{EYY} are the Bernoulli measures. In this paper, we extend the universality result of cite{EYY} to include the Bernoulli measures so that the only restrictions on the probability distributions of the matrix elements are the subexponential decay and the normalization condition that the variances in each row sum up to one. The new ingredient is a strong local semicircle law which improves the error estimate on the Stieltjes transform of the empirical measure of the eigenvalues from the order $(N eta)^{-1/2}$ to $(N eta)^{-1}$. Here $eta$ is the imaginary part of the spectral parameter in the definition of the Stieltjes transform and $N$ is the size of the matrix." @default.
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• W2037413976 date "2010-03-19" @default.
• W2037413976 modified "2023-10-18" @default.
• W2037413976 title "Universality for generalized Wigner matrices with Bernoulli distribution" @default.
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• W2037413976 doi "https://doi.org/10.48550/arxiv.1003.3813" @default.
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