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4 papers · 2 filters
Bulk Universality for Wigner Matrices
Laszlo Erdos, Sandrine Peche, Jose A. Ramirez +2
We consider Hermitian Wigner random matrices where the probability density for each matrix element is given by the density . We prove that the eig…
An extension of the Duistermaat-Singer Theorem to the semi-classical Weyl algebra
Yves Colin De Verdière
Motivated by many recent works (by L. Charles, V. Guillemin, T. Paul, J. Sjöstrand, A. Uribe, S. Vu Ngoc, S. Zelditch and others) on the semi-classical Birkhoff normal forms, we in…
The semi-classical spectrum and the Birkhoff normal form
Yves Colin De Verdière
The purposes of this note are: 1) to propose a direct and "elementary" proof of the main result proved by Guillemin-Paul-Uribe [GPU], namely that the semi-classical spectrum near a…
Modes and quasi-modes on surfaces: variation on an idea of Andrew Hassell
Yves Colin De Verdière
This paper is inspired from the nice result of Andrew Hassell on the eigenfunctions in the stadium billiard. From a classical paper of V. Arnol'd, we know that quasi-modes are not…