Communications in Mathematical Physics

, Volume 199, Issue 3, pp 683–695

A Note on the Eigenvalue Density of Random Matrices

  • Michael K.-H. Kiessling
  • Herbert Spohn

DOI: 10.1007/s002200050516

Cite this article as:
Kiessling, M. & Spohn, H. Comm Math Phys (1999) 199: 683. doi:10.1007/s002200050516

Abstract:

The distribution of eigenvalues of N×N random matrices in the limit N→∞ 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.

Copyright information

©  1999

Authors and Affiliations

  • Michael K.-H. Kiessling
    • 1
  • Herbert Spohn
    • 1
  1. 1.Department of Mathematics, Rutgers University, 110 Frelinghuysen Rd., Piscataway, N.J. 08854, USA.¶E-mail: miki@math.rutgers.eduUS