Some Asymptotic Properties of the Spectrum of the Jacobi Ensemble

Pathwise asymptotic behavior of random determinants in the Jacobi ensemble

This is a companion paper of [Rou05]. It concentrates on asymptotic properties of determinants of some random matrices in the Jacobi ensemble. Let M ∈ Mn1+n2,r(R) (with r ≤ n1 + n2) be a random matrix whose entries are standard i.i.d. Gaussian. We can decompose MT = (MT 1 ,M T 2 ) with M1 ∈ Mn1,r and M2 ∈ Mn2,r. Then, W1 := MT 1 M1 and W2 := MT 2 M2 are independent r× r Wishart matrices with pa...

On the Spectral Properties of Degenerate Non-selfadjoint Elliptic systems of Differential Operators

Asymptotic properties of the sample mean in adaptive sequential sampling with multiple selection criteria

‎We extend the method of adaptive two-stage sequential sampling to‎‎include designs where there is more than one criteria is used in‎‎deciding on the allocation of additional sampling effort‎. ‎These‎‎criteria‎, ‎or conditions‎, ‎can be a measure of the target‎‎population‎, ‎or a measure of some related population‎. ‎We develop‎‎Murthy estimator for the design that is unbiased estimators for‎‎t...

Extended Jacobi and Laguerre Functions and their Applications

The aim of this paper is to introduce two new extensions of the Jacobi and Laguerre polynomials as the eigenfunctions of two non-classical Sturm-Liouville problems. We prove some important properties of these operators such as: These sets of functions are orthogonal with respect to a positive de nite inner product de ned over the compact intervals [-1, 1] and [0,1), respectively and also th...

Some Results for the Jacobi-Dunkl Transform in the Space $L^{p}(mathbb{R},A_{alpha,beta}(x)dx)$

In this paper, using a generalized Jacobi-Dunkl translation operator, we obtain a generalization of Titchmarsh's theorem for the Dunkl transform for functions satisfying the Lipschitz Jacobi-Dunkl condition in the space Lp.