Abstract This paper is concerned with the explicit computation of limiting distribution function largest real eigenvalue in Ginibre ensemble when each has been removed independently constant likelihood. We show that recently discovered integrable structures [2] generalize from to its thinned equivalent. Concretely, we express aforementioned as a convex combination two simple Fredholm determinan...

In this paper, we employ transformation operators and Levinson’s density formula to study the distribution of interior transmission eigenvalues for a spherically stratified media. In particular, we show that under smoothness condition on the index of refraction that there exist an infinite number of complex eigenvalues and there exist situations when there are no real eigenvalues. We also consi...

A truncation of a Haar distributed orthogonal random matrix gives rise to a matrix whose eigenvalues are either real or complex conjugate pairs, and are supported within the closed unit disk. This is also true for a product Pm of m independent truncated orthogonal random matrices. One of most basic questions for such asymmetric matrices is to ask for the number of real eigenvalues. In this pape...

The statistical properties of trajectories of eigenvalues of Gaussian complex matrices whose Hermitian condition is progressively broken are investigated. It is shown how the ordering on the real axis of the real eigenvalues is reflected in the structure of the trajectories and also in the final distribution of the eigenvalues in the complex plane.

This paper concerns the transmission eigenvalue problem for an inhomogeneous media of compact support containing small penetrable homogeneous inclusions. Assuming that the inhomogeneous background media is known and smooth, we investigate how these small volume inclusions affect the real transmission eigenvalues. Note that for practical applications the real transmission eigenvalues are importa...

In this paper, we investigate the consistency and asymptotic efficiency of an estimator of the drift matrix, F , of Ornstein-Uhlenbeck processes that are not necessarily stable. We consider all the cases. (1) The eigenvalues of F are in the right half space (i.e., eigenvalues with positive real parts). In this case the process grows exponentially fast. (2) The eigenvalues of F are on the left h...

In this paper, we define the symmetric hyperdeterminant, eigenvalues and E-eigenvalues of a real supersymmetric tensor. We show that eigenvalues are roots of a one-dimensional polynomial, and when the order of the tensor is even, E-eigenvalues are roots of another one-dimensional polynomial. These two one-dimensional polynomials are associated with the symmetric hyperdeterminant. We call them t...

The structure of eigenvalues of −y q x y λy, y 0 0, and y 1 ∑m k 1 αky ηk , will be studied, where q ∈ L1 0, 1 ,R , α αk ∈ R, and 0 < η1 < · · · < ηm < 1. Due to the nonsymmetry of the problem, this equation may admit complex eigenvalues. In this paper, a complete structure of all complex eigenvalues of this equation will be obtained. In particular, it is proved that this equation has always a ...