ASYMPTOTIC DISTRIBUTION OF EIGENVALUES AND DEGENERATION OF SPARSE RANDOM MATRICES

Asymptotic Distribution of Eigenvalues and Degeneration of Sparse Random Matrices

This work is concerned with an asymptotical distribution of eigenvalues of sparse random matrices. It is shown that the semicircle law which is known for random matrices is also valid for the sparse random matrices with sparsity nIN=o(1), where n is the matrix size and 2N the number of non-zero elements of the matrix. The degree of degeneration is also estimated for the matrices with 2N—cn (c>0...

Asymptotic distribution of eigenvalues of the elliptic operator system

Since the theory of spectral properties of non-self-accession differential operators on Sobolev spaces is an important field in mathematics, therefore, different techniques are used to study them. In this paper, two types of non-self-accession differential operators on Sobolev spaces are considered and their spectral properties are investigated with two different and new techniques.

Distribution of Eigenvalues for Some Sets of Random Matrices

Eigenvalues of Euclidean random matrices

We study the spectral measure of large Euclidean random matrices. The entries of these matrices are determined by the relative position of n random points in a compact set Ωn of R. Under various assumptions we establish the almost sure convergence of the limiting spectral measure as the number of points goes to infinity. The moments of the limiting distribution are computed, and we prove that t...

asymptotic property of order statistics and sample quntile

چکیده: فرض کنید که تابعی از اپسیلون یک مجموع نامتناهی از احتمالات موزون مربوط به مجموع های جزئی براساس یک دنباله از متغیرهای تصادفی مستقل و همتوزیع باشد، و همچنین فرض کنید توابعی مانند g و h وجود دارند که هرگاه امید ریاضی توان دوم x متناهی و امیدریاضی x صفر باشد، در این صورت می توان حد حاصلضرب این توابع را بصورت تابعی از امید ریاضی توان دوم x نوشت. حالت عکس نیز برقرار است. همچنین ما با استفاده...