Convergence rate of extremes from Maxwell sample

Asymptotic expansions for distributions of extremes from generalized Maxwell distribution

In this paper, with optimal normalized constants, the asymptotic expansions of the distribution of the normalized maxima from generalized Maxwell distribution is derived. It shows that the convergence rate of the normalized maxima to the Gumbel extreme value distribution is proportional to 1/ log n.

The rate of convergence of spectra of sample covariance matrices

It is shown that the Kolmogorov distance between the spectral distribution function of a random covariance matrix 1 p XX T , where X is a n × p matrix with independent entries and the distribution function of the Marchenko-Pastur law is of order O(n −1/2). The bounds hold uniformly for any p, including p n equal or close to 1.

On convergence of sample and population Hilbertian functional principal components

In this article we consider the sequences of sample and population covariance operators for a sequence of arrays of Hilbertian random elements. Then under the assumptions that sequences of the covariance operators norm are uniformly bounded and the sequences of the principal component scores are uniformly sumable, we prove that the convergence of the sequences of covariance operators would impl...

High frequency behavior of the Maxwell-Bloch model with relaxation: convergence to the Schrödinger-rate system

We study the Maxwell-Bloch model, which describes the propagation of a laser through a material and the associated interaction between laser and matter (polarization of the atoms through light propagation, photon emission and absorption, etc.). The laser field is described through Maxwell’s equations, a classical equation, while matter is represented at a quantum level and satisfies a quantum L...

Smoothing sample extremes: The mixed model approach