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The eigenvalue spectrum of a large symmetric random matrix

1976; Institute of Physics; Volume: 9; Issue: 10 Linguagem: Inglês

10.1088/0305-4470/9/10/011

1361-6447

S. F. Edwards, R C Jones,

Stochastic processes and statistical mechanics

A new and straightforward method is presented for calculating the eigenvalue spectrum of a large symmetric square matrix each of whose upper triangular elements is described by a Gaussian probability density function with the same mean and variance. Using the n to 0 method, the authors derive the semicircular eigenvalue spectrum when the mean of each element is zero and show that there is a critical finite mean value above which a single eigenvalue splits off from the semicircular continuum of eigenvalues.