caa a22 4500 605524696 CHVBK 20210128100755.0 cr unu---uuuuu 210128e20150101xx s 000 0 eng 10.1007/s10958-014-2192-5 doi (NATIONALLICENCE)springer-10.1007/s10958-014-2192-5 Naumov A. Moscow State University, Moscow, Russia aut Limit Theorems for Two Classes of Random Matrices with Gaussian Entries [Elektronische Daten] [A. Naumov] In this note, we consider ensembles of random symmetric matrices with Gaussian elements. Assume that E $$ \mathbb{E} $$ X ij = 0 and E X i j 2 = σ i j 2 $$ \mathbb{E}{X}_{ij}^2={\sigma}_{ij}^2 $$ We do not assume that all the σ ij are equal. Assuming that the average of the normalized sums of variances in each row converges to one and the Lindeberg condition holds, we prove that the empirical spectral distribution of eigenvalues converges to Wigner's semicircle law. We also provide an analogue of this result for sample covariance matrices and prove the convergence to the Marchenko-Pastur law. Bibliography: 5 titles. Springer Science+Business Media New York, 2014 Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 204/1(2015-01-01), 140-147 1072-3374 204:1<140 2015 204 10958 https://doi.org/10.1007/s10958-014-2192-5 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10958-014-2192-5 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Naumov A. Moscow State University, Moscow, Russia aut NATIONALLICENCE 773 0- Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 204/1(2015-01-01), 140-147 1072-3374 204:1<140 2015 204 10958