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Universality of the local eigenvalue statistics for a class of unitary invariant random matrix ensembles

Journal Article · · Journal of Statistical Physics
DOI:https://doi.org/10.1007/BF02180200· OSTI ID:468663
 [1];  [2]
  1. Institute for Low Temperature Physics, Kharkov (Ukraine)
  2. Institute of Low Temperature Physics, Kharkov (Ukraine)
This paper is devoted to the rigorous proof of the universality conjecture of random matrix theory, according to which the limiting eigenvalue statistics of n x n random matrices within spectral intervals of O(n{sup -1}) is determined by the type of matrix (real symmetric, Hermitian, or quaternion real) and by the density of states. We prove this conjecture for a certain class of the Hermitian matrix ensembles that arise in the quantum field theory and have the unitary invariant distribution defined by a certain function (the potential in the quantum field theory) satisfying some regularity conditions.
Sponsoring Organization:
USDOE
OSTI ID:
468663
Journal Information:
Journal of Statistical Physics, Journal Name: Journal of Statistical Physics Journal Issue: 1-2 Vol. 86; ISSN JSTPBS; ISSN 0022-4715
Country of Publication:
United States
Language:
English

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