# Accession Number:

## ADA160209

# Title:

## Limiting Behavior of the Norm of Products of Random Matrices and Two Problems of Geman-Hwang.

# Descriptive Note:

## Technical rept.,

# Corporate Author:

## PITTSBURGH UNIV PA CENTER FOR MULTIVARIATE ANALYSIS

# Report Date:

## 1984-11-01

# Pagination or Media Count:

## 25.0

# Abstract:

In the theory of large random matrices, how to dominate the norm of a random matrix is a very important problem. This paper considers a different type of random matrices, namely -W to the k power, i.e. a power of a square random matrix with iid entries. The first result in this paper is the limit as n approaches infinity of the absolute value of Wsq rt. n to the k power is or 1ksigma to the k power where n is the size of W and here sigma-sq. is the variance of the entries of W. We assume only the existence of the 4-th moment of the entries of W. From this result it is easy to show that the spectral radius of W sq rt n is not greater then -sigma with probability 1. This result is known only for iid NO,-sigma-sq case. In proving the above result, a new kind of graphs has to be discussed carefully, and the truncation method used in Yin-Bai-Krishnaiah is also important here.

# Descriptors:

# Subject Categories:

- Theoretical Mathematics