Random discrete Schrödinger operators from random matrix theory

Random discrete Schrödinger operators from Random Matrix Theory

We investigate random, discrete Schrödinger operators which arise naturally in the theory of random matrices, and depend parametrically on Dyson’s Coulomb gas inverse temperature β. They are similar to the class of “critical” random Schrödiner operators with random potentials which diminish as |x|− 12 . We show that as a function of β they undergo a transition from a regime of (power-law) local...

Random matrix theory

Random matrix theory is now a big subject with applications in many disciplines of science, engineering and finance. This article is a survey specifically oriented towards the needs and interests of a numerical analyst. This survey includes some original material not found anywhere else. We include the important mathematics which is a very modern development, as well as the computational softwa...

Random Matrix Theory

Random matrix theory is usually taught as a sequence of several graduate courses; we have 16 lectures, so we will give a very brief introduction. Some relevant books for the course: • G. Anderson, A. Guionnet, O. Zeitouni. An introduction to random matrices. [1] • A. Guionnet. Large random matrices: lectures on macroscopic asymptotics. • M. L. Mehta. Random matrices. The study of random matrice...

Random Matrix Theory

Estimating Unknown Spins from Random Matrix Theory

The neutron resonances, especially in heavy fissioning nuclei, were extensively studied during last 60 years. The renewed interest to their properties is related to the problem of quantum chaos. In the region of low neutron energies, the resonances are very narrow and well separated. The large lifetime and the small energy spread allow one to interpret a resonance as a fully equilibrated compou...