ISSN:
1572-9613
Schlagwort(e):
Random matrices
;
local asymptotic regime
;
universality conjecture
;
orthogonal polynomial technique
Quelle:
Springer Online Journal Archives 1860-2000
Thema:
Physik
Notizen:
Abstract This paper is devoted to the rigorous proof of the universality conjecture of random matrix theory, according to which the limiting eigenvalue statistics ofn×n random matrices within spectral intervals ofO(n −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.
Materialart:
Digitale Medien
URL:
http://dx.doi.org/10.1007/BF02180200
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