@article{2782,
abstract = {We consider random n×n matrices of the form (XX*+YY*)^{-1/2}YY*(XX*+YY*)^{-1/2}, where X and Y have independent entries with zero mean and variance one. These matrices are the natural generalization of the Gaussian case, which are known as MANOVA matrices and which have joint eigenvalue density given by the third classical ensemble, the Jacobi ensemble. We show that, away from the spectral edge, the eigenvalue density converges to the limiting density of the Jacobi ensemble even on the shortest possible scales of order 1/n (up to log n factors). This result is the analogue of the local Wigner semicircle law and the local Marchenko-Pastur law for general MANOVA matrices.},
author = {Erdös, László and Farrell, Brendan},
journal = {Journal of Statistical Physics},
number = {6},
pages = {1003 -- 1032},
publisher = {Springer},
title = {{Local eigenvalue density for general MANOVA matrices}},
doi = {10.1007/s10955-013-0807-8},
volume = {152},
year = {2013},
}
@article{2837,
abstract = {We consider a general class of N × N random matrices whose entries hij are independent up to a symmetry constraint, but not necessarily identically distributed. Our main result is a local semicircle law which improves previous results [17] both in the bulk and at the edge. The error bounds are given in terms of the basic small parameter of the model, maxi,j E|hij|2. As a consequence, we prove the universality of the local n-point correlation functions in the bulk spectrum for a class of matrices whose entries do not have comparable variances, including random band matrices with band width W ≫N1-εn with some εn > 0 and with a negligible mean-field component. In addition, we provide a coherent and pedagogical proof of the local semicircle law, streamlining and strengthening previous arguments from [17, 19, 6].},
author = {Erdös, László and Knowles, Antti and Yau, Horng and Yin, Jun},
journal = {Electronic Journal of Probability},
number = {59},
pages = {1--58},
publisher = {Institute of Mathematical Statistics},
title = {{The local semicircle law for a general class of random matrices}},
doi = {10.1214/EJP.v18-2473},
volume = {18},
year = {2013},
}