Number of energy levels outside Wigner's semicircle
- 21 December 1983
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 16 (18) , L767-L769
- https://doi.org/10.1088/0305-4470/16/18/016
Abstract
The total probability outside Wigner's (1962) semicircle is calculated using Mehler's formula for the Hermite polynomials. In the limit N to infinity , N being the dimension of the random Gaussian Hermitian matrix it is shown that this probability is 0.05N-32/. Some implications of this small probability are discussed.Keywords
This publication has 3 references indexed in Scilit:
- On the expansion of the single eigenvalue probability density functionJournal of Statistical Physics, 1981
- The eigenvalue spectrum of a large symmetric random matrixJournal of Physics A: General Physics, 1976
- Accuracy of the Semicircle Approximation for the Density of Eigenvalues of Random MatricesJournal of Mathematical Physics, 1964