0 60 20 01 v 1 3 1 Ja n 20 06 Eigenvalue distributions for some correlated complex sample covariance matrices

ar X iv : m at h / 06 01 74 3 v 1 [ m at h . SP ] 3 0 Ja n 20 06 DETERMINANTS OF ZEROTH ORDER OPERATORS

Tracy-Widom limit for the largest eigenvalue of a large class of complex Wishart matrices

The problem of understanding the limiting behavior of the largest eigenvalue of sample covariance matrices computed from data matrices for which both dimensions are large has recently attracted a lot of attention. In this paper we consider the following type of complex sample covariance matrices. Let X be an n×p matrix, and let its rows be i.i.d NC(0,Σp). We denote byHp the spectral distributio...

ar X iv : n uc l - th / 0 60 10 68 v 1 2 4 Ja n 20 06 Neutrino - nucleus reactions in the energy range 1 - 100 MeV

We review some salient aspects of calculations of the neutrino-nucleus reaction cross sections in the low energy range (1-100 MeV).

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...

ar X iv : m at h . A C / 0 60 17 31 v 2 3 1 Ja n 20 06 ON POLYNOMIAL

Let Φ(x, y) be a bivariate polynomial with complex coefficients. The zeroes of Φ(x, y) are given a combinatorial structure by considering them as arcs of a directed graph G(Φ). This paper studies some relationship between the polynomial Φ(x, y) and the structure of G(Φ).