Random right eigenvalues of Gaussian quaternionic matrices

The spherical law (analogously to the circular law) states that the eigenvalues have uniform density on a sphere (under stereographic projection) in the limit of large matrix

We exhibit an explicit formula for the spectral density of a (large) random matrix which is a diagonal matrix whose spectral density converges, perturbated by the addition of

It was shown under sev- eral hypotheses in [ 77 , 43 , 28 , 29 , 19 , 20 , 16 , 17 , 30 , 61 , 62 ] that for a large random Hermitian matrix, if the strength of the added

This result gives an understanding of the simplest and fastest spectral method for matrix alignment (or complete weighted graph alignment), and involves proof methods and

Large random matrices, Stieltjes transform of positive matrix- valued measures, Hankel matrices.. The different blocks

Much study has been devoted to the eigenvalues of random unitary matrices, but little is known about the entries of random unitary matrices and their powers.. In this work, we

We establish a large deviation principle for the empirical spec- tral measure of a sample covariance matrix with sub-Gaussian entries, which extends Bordenave and Caputo’s result

Central limit theorem for linear eigenvalue statistics of the Wigner and sample covariance random matrices. Strong convergence of the empirical distribution of eigenvalues