A Note on the Eigenvalue Density of Random Matrices

Details A Note on the Eigenvalue Density of Random Matrices A Note on the Eigenvalue Density of Random Matrices

1998-04-04

arxiv.org/abs/math-ph/9804006v3

Commun. Math. Phys. 199, pp. 683-695 (1999)

Physics

Mathematical Physics

20 pages, revised version (a minor correction in sect. 3; small corrections in examples 3 and 4 in sect.IV; references updated

Scientific paper

10.1007/s002200050516

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.

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