We report briefly on an application of random matrix theory to the analysis of SA financial market data (An Analysis of cross-correlations in South African financial market data, e- print cond-mat/0402389). Correlation matrices C are constructed from 10 years of daily data for stocks listed on...

We consider the logarithm of the characteristic polynomial of random permutation matrices, evaluated on a finite set of different points. The permutations are chosen with respect to the Ewens distribution on the symmetric group. We show that the behavior at different points is independent in the...

We study the problem of nonparametric regression when the regressor is endogenous, which is an important nonparametric instrumental variables (NPIV) regression in econometrics and a difficult ill-posed inverse problem with unknown operator in statistics. We first establish a general upper bound...

In this paper we present the asymptotic theory for spectral distributions of high dimensional covariation matrices of Brownian diffusions. More specifically, we consider N-dimensional Itô integrals with time varying matrix-valued integrands. We observe n equidistant high frequency data points...

The probability of small deviations of the determinant of the matrix AAT is estimated, where A is an n×∞ random matrix with centered entries having the joint Gaussian distribution. The inequality obtained is sharp in a sense.

We consider the moment space MnK corresponding to p×p complex matrix measures defined on K (K=[0,1] or K=T). We endow this set with the uniform distribution. We are mainly interested in large deviation principles (LDPs) when n→∞. First we fix an integer k and study the vector of the first k...

In this paper we define distributions on the moment spaces corresponding to p×p real or complex matrix measures on the real line with an unbounded support. For random vectors on the unbounded matricial moment spaces we prove the convergence in distribution to the Gaussian orthogonal ensemble or...

It is known (Hofmann-Credner and Stolz (2008) [4]) that the convergence of the mean empirical spectral distribution of a sample covariance matrix Wn=1/nYnYnt to the Marčenko–Pastur law remains unaffected if the rows and columns of Yn exhibit some dependence, where only the growth of the...

The statistics of the eigenvalues of symmetric random matrices, composed by real and statistically independent elements following the distribution that maximizes Tsallis's entropy, is carried numerically in the limit of large matrices. For entropic indexes in the interval −∞<q<53, by using a convenient rescale of variables, it is possible to show that such matrices fall in the same class of the Gaussian orthogonal ensemble (GOE). For the entropic index 53⩽q<3, the density of eigenvalues and the distribution of level spacings do not seem to follow a simple rescale of variables involving different values of q, and exhibit a behavior very distinct from the GOE: both quantities present long tails for 53⩽q⩽2, and such long tails die out when q>2. The density of...</q<53,>