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math.PR2020★ 4 cited
Two-sided inequalities for the density function's maximum of weighted sum of chi-square variables
Sergey G. Bobkov, Alexey A. Naumov, Vladimir V. Ulyanov
Two--sided bounds are constructed for a probability density function of a weighted sum of chi-square variables. Both cases of central and non-central chi-square variables are consi…
math.PR2019
Local semicircle law under fourth moment condition
Friedrich Götze, Alexey Naumov, Alexander Tikhomirov
We consider a random symmetric matrix with upper triangular entries being independent random variables with mean zero and unit variance. Assuming tha…
math.PR2012★ 18 cited
Semicircle Law for a Class of Random Matrices with Dependent Entries
F. Götze, A. Naumov, A. Tikhomirov
In this paper we study ensembles of random symmetric matrices $\X_n = {X_{ij}}_{i,j = 1}^n$ with dependent entries such that $\E X_{ij} = 0$, $\E X_{ij}^2 = σ_{ij}^2$, where $σ_{ij…