18 citations · 32 across the 6 of their papers we have counts for
6 papers
Local Laws for Sparse Sample Covariance Matrices without the truncation condition
F. Götze, A. Tikhomirov, D. Timushev
We consider sparse sample covariance matrices , where is a sparse matrix of order with the sparse probability . We pr…
On the Largest and the Smallest Singular Value of Sparse Rectangular Random Matrices
F. Götze, A. Tikhomirov
We derive estimates for the largest and smallest singular values of sparse rectangular random matrices, assuming . We consider a…
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…
On the Rate of Convergence to the Marchenko--Pastur Distribution
F. Götze, A. Tikhomirov
Let denote random matrix with entries , which are independent for . We consider the rate of convergence of empiric…
On the rate of convergence to the semi-circular law
Friedrich Götze, Alexander Tikhomirov
Let denote a Hermitian random matrix with entries , which are independent for . We consider the rate of convergence of the empirical spect…
On the Circular Law
F. Götze, A. Tikhomirov
We consider the joint distribution of real and imaginary parts of eigenvalues of random matrices with independent real entries with mean zero and unit variance. We prove the conver…