The Wigner semi-circle law and the Heisenberg group

• Autorzy: Jacques Faraut , Linda Saal
• Języki publikacji: EN

Abstrakty

EN

The Wigner Theorem states that the statistical distribution of the eigenvalues of a random Hermitian matrix converges to the semi-circular law as the dimension goes to infinity. It is possible to establish this result by using harmonic analysis on the Heisenberg group. In fact this convergence corresponds to the topology of the set of spherical functions associated to the action of the unitary group on the Heisenberg group.

Kategorie tematyczne

• 26A46: Absolutely continuous functions
• 43A90: Spherical functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2007
• Tom: 78
• Numer: 1
• Strony: 133-143

Daty

wydano

2007

Twórcy

autor

Jacques Faraut

• Institut de Mathématiques de Jussieu, Université Pierre et Marie Curie, 175 rue du Chevaleret, 75013 Paris, France

autor

Linda Saal

• Facultad de Matemática, Astronomía y Física, Universidad Nacional de Córdoba, 5000 Córdoba, Argentina

Identyfikatory

DOI

10.4064/bc78-0-9