Limiting Spectral Distribution for a Class of Random Matrices.
Abstract
A new combinatorial technique was developed in a previous paper to prove the existence of a limiting spectral distribution. That work can be generalized in two directions. First, we can generalize to the case when X sub P has isotropic columns. This work was done in Yin and Krishnaiah and Bai, Yin, and Krishnaiah. In the second direction, we can prove the result by assuming that X sub p has i.i.d. entries with minimum moment requirements. This paper is devoted to this goal. In this paper, we have succeeded to prove the existence of limiting spectral distribution by assuming only that the second moment exists. The keys to reach this goal are (1) truncation technique and (2) sophisticated combinatorial techniques. The two-stage truncation method works in proving the main result. To prove the main result, we have to generalize the notion of Q-graph to a new kind of graphs - M-graphs. Some properties of M-graphs are developed here. In this paper, we have succeeded to prove the existence of the limiting spectral distribution in the sense of a.s. convergence. Keywords: multivariate F matrix.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1984
- Accession Number
- ADA161059
Entities
People
- Y. Q. Yin
Organizations
- University of Pittsburgh