# A new classification scheme for Random Matrix Theories

@article{Caselle1996ANC, title={A new classification scheme for Random Matrix Theories}, author={Michele Caselle}, journal={arXiv: Statistical Mechanics}, year={1996} }

In the last few years several new Random Matrix Models have been proposed and studied. They have found application in various different contexts, ranging from the physics of mesoscopic systems to the chiral transition in lattice gauge theory. These new ensembles can be classified in terms of the same Dynkin diagrams and root lattices which are used in the classification of the Lie algebras.

## 12 Citations

Random matrix theory and symmetric spaces

- Physics, Mathematics
- 2004

Abstract In this review we discuss the relationship between random matrix theories and symmetric spaces. We show that the integration manifolds of random matrix theories, the eigenvalue distribution,…

The supersymmetric technique for random-matrix ensembles with zero eigenvalues

- Physics
- 2002

The supersymmetric technique is applied to computing the average spectral density near zero energy in the large-N limit of the random-matrix ensembles with zero eigenvalues: B, DIII-odd, and the…

A generalization of random matrix ensemble, I: General theory

- Mathematics, Physics
- 2005

We give a generalization of random matrix ensembles, which includes all classical ensembles. We derive the joint-density function of the generalized ensemble by one simple formula, giving a direct…

Random matrices beyond the Cartan classification

- Physics, Mathematics
- 2008

It is known that hermitean random matrix ensembles can be identified with symmetric coset spaces of Lie groups, or else with tangent spaces of the same. This results in a classification of random…

Disordered Quantum Wires: Microscopic Origins of the DMPK Theory and Ohm’s Law

- Physics, Mathematics
- 2012

We study the electronic transport properties of the Anderson model on a strip, modeling a quasi one-dimensional disordered quantum wire. In the literature, the standard description of such wires is…

Random-Matrix Ensembles in p-Wave Vortices

- Physics
- 2002

In disordered vortices in p-wave superconductors the two new random-matrix ensembles may be realized: B and DIII-odd (of so(2N + 1) and so(4N + 2)/u(2N + 1) matrices respectively). We predict these…

Universal broadening of zero modes: A general framework and identification.

- Physics, MedicinePhysical review. E
- 2019

It is shown that the corresponding eigenvalues of perturbed Hermitian operators with zero modes broaden to a Gaussian random matrix ensemble of size ν×ν, where ν is the number of zero modes.

Satake diagrams of affine Kac?Moody algebras

- Mathematics
- 2006

Satake diagrams of affine Kac–Moody algebras (untwisted and twisted) are obtained from their Dynkin diagrams. These diagrams give a classification of restricted root systems associated with these…

Théorie des matrices aléatoires en physique statistique : théorie quantique de la diffusion et systèmes désordonnés

- Physics
- 2018

Random matrix theory has applications in various fields: mathematics, physics, finance, ... In physics, the concept of random matrices has been used to study the electronic transport in mesoscopic…

LANGLANDS DECOMPOSITION OF AFFINE KAC-MOODY ALGEBRAS

- Mathematics
- 2007

Langlands decompositions of affine Kac-Moody algebras have been obtained by the method of direct determination as introduced by Cornwell for Lie algebras. This method is particularly helpful in the…

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