A Note on the Eigenvalue Density of Random Matrices
Mathematical Physics
2009-10-31 v3 math.MP
Probability
Abstract
The distribution of eigenvalues of N times N random matrices in the limit N to infinity is the solution to a variational principle that determines the ground state energy of a confined fluid of classical unit charges. This fact is a consequence of a more general theorem, proven here, in the statistical mechanics of unstable interactions. Our result establishes the eigenvalue density of some ensembles of random matrices which were not covered by previous theorems.
Cite
@article{arxiv.math-ph/9804006,
title = {A Note on the Eigenvalue Density of Random Matrices},
author = {Michael K. -H. Kiessling and Herbert Spohn},
journal= {arXiv preprint arXiv:math-ph/9804006},
year = {2009}
}
Comments
20 pages, revised version (a minor correction in sect. 3; small corrections in examples 3 and 4 in sect.IV; references updated; Comments of L. Pastur and P. Zinn-Justin incorporated), to appear in: Commun. Math. Phys