Large deviations for random matrix ensembles in mesoscopic physics

Abstract

In his seminal 1962 paper on the ``threefold way'', Freeman Dyson classified the spaces of matrices that support the random matrix ensembles deemed relevant from the point of view of classical quantum mechanics. Recently, Heinzner, Huckleberry and Zirnbauer have obtained a similar classification based on less restrictive assumptions, thus taking care of the needs of modern mesoscopic physics. Their list is in one-to-one correspondence with the infinite families of Riemannian symmetric spaces as classified by Cartan. The present paper develops the corresponding random matrix theories, with a special emphasis on large deviation principles.

21 pages

References in corpus (4)

• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Random Matrix Theory of a Chaotic Andreev Quantum Dot
• Random matrix theory and symmetric spaces
• Large deviations and stochastic calculus for large random matrices

Cited by in corpus (6)

• Orbit measures, random matrix theory and interlaced determinantal processes
• Borel theorems for random matrices from the classical compact symmetric spaces
• Canonical moments and random spectral measures
• Large deviations for disordered bosons and multiple orthogonal polynomial ensembles
• Large deviations for the largest eigenvalue of disordered bosons and disordered fermionic systems
• Brownian motion in a truncated Weyl chamber