THE INVERSION FORMULA OF THE STIELTJES TRANSFORM OF SPECTRAL DISTRIBUTION

• 발행기관: 충청수학회
• 저자명: Sang Il Choi
• 간행물 정보: 『Journal of the Chungcheong Mathematical Society』Volume 22, No. 3, 519~524쪽, 전체 6쪽
• 주제분류: 자연과학 > 자연과학일반
• 파일형태: PDF
• 발행일자: 2009.09.30

영문 초록

In multivariate analysis, the inversion formula of the Stieltjes transform is used to ¯nd the density of a spectral distribution of random matrices of sample covariance type. Let Bn = 1 nY Tm TmYm where Ym =[Yij ]m£n is with independent, identically distributed entries and Tm is an m £ m symmetric nonnegative de¯nite random matrix independent of the Yij s. In the present paper, using the inversion formula of the Stieltjes transform, we will ¯nd the density function of the limiting distribution of Bn away from zero.

목차

1. Introduction

2. Stieltjes transform and inversion formula

References