Comparison theorem for some extremal eigenvalue statistics

Universality of Local Eigenvalue Statistics for Some Sample Covariance Matrices

Abstract We consider random, complex sample covariance matrices 1 N X ∗X , where X is a p×N random matrix with i.i.d. entries of distribution μ. It has been conjectured that both the distribution of the distance between nearest neighbor eigenvalues in the bulk and that of the smallest eigenvalues become, in the limit N → ∞, p N → 1, the same as that identified for a complex Gaussian distributio...

EXTREMAL EIGENVALUE PROBLEMS FOR THE LAPLACIANSteven

The extremal spheres theorem

Consider a polygon P and all neighboring circles (circles going through three consecutive vertices of P ). We say that a neighboring circle is extremal if it is empty (no vertices of P inside) or full (no vertices of P outside). It is well known that for any convex polygon there exist at least two empty and at least two full circles, i.e. at least four extremal circles. In 1990 Schatteman consi...

Statistics of extremal intensities for Gaussian interfaces.

The extremal Fourier intensities are studied for stationary Edwards-Wilkinson-type, Gaussian, interfaces with power-law dispersion. We calculate the probability distribution of the maximal intensity and find that, generically, it does not coincide with the distribution of the integrated power spectrum (i.e., roughness of the surface), nor does it obey any of the known extreme statistics limit d...

Central limit theorem for linear eigenvalue statistics of orthogonally invariant matrix models

We prove central limit theorem for linear eigenvalue statistics of orthogonally invariant ensembles of randommatrices with one interval limiting spectrum. We consider ensembles with real analytic potentials and test functions with two bounded derivatives.