The eigenvalue spectrum of a large symmetric random matrix with a finite mean

Abstract

A recently published Letter by Kota and Potbhare (1977) obtains the averaged spectrum of a large symmetric random matrix each element of which has a finite mean: their results disagree with two recent calculations which predict that under certain circumstances a single isolated eigenvalue splits off from the continuous semicircular distribution of eigenvalues associated with the random part of the matrix. This letter offers a simple re-derivation of this result and corrects the error in the work of Kota and Potbhare.