Communications in Mathematical Physics

, Volume 199, Issue 3, pp 683-695

First online:

A Note on the Eigenvalue Density of Random Matrices

  • Michael K.-H. KiesslingAffiliated withDepartment of Mathematics, Rutgers University, 110 Frelinghuysen Rd., Piscataway, N.J. 08854, USA.¶E-mail: miki@math.rutgers.edu
  • , Herbert SpohnAffiliated withDepartment of Mathematics, Rutgers University, 110 Frelinghuysen Rd., Piscataway, N.J. 08854, USA.¶E-mail: miki@math.rutgers.edu

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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.