Quantitative version of a Silverstein's result

TL;DR

This paper provides a quantitative enhancement of Silverstein's theorem, establishing probabilistic bounds on the norm of random matrices with i.i.d. entries under natural conditions.

Contribution

It introduces a quantitative version of Silverstein's theorem, offering explicit probabilistic bounds for the matrix norm convergence.

Findings

Probabilistic bounds on matrix norm for i.i.d. entries

Conditions under which the matrix norm is not small with high probability

Extension of Silverstein's theorem to quantitative estimates

Abstract

We prove a quantitative version of a Silverstein's Theorem on a condition for convergence in probability of the norm of random matrix. More precisely, we show that for a random matrix whose entries are i.i.d. random variables, $w_{i,j}$, satisfying certain natural conditions, is not small with large probability.