Random Matrices and the Anderson Model

TL;DR

This paper reviews recent advances in applying renormalization group and supersymmetric methods to analyze the Anderson Model, highlighting its connection to random matrix theory and focusing on spectral properties.

Contribution

It provides a comprehensive review of the application of constructive field techniques and supersymmetry to the Anderson Model, elucidating its link with random matrices.

Findings

Clarified the relationship between the Anderson Model and random matrix theory

Reviewed the use of supersymmetric formalism in analyzing spectral properties

Outlined current research programs on density of states and Green's functions

Abstract

In recent years,constructive field techniques and the method of renormalization group around extended singularities have been applied to the weak coupling regime of the Anderson Model. It has allowed to clarify the relationship between this model and the theory of random matrices. We review this situation and the current program to analyze in detail the density of states and Green's functions of this model using the supersymmetric formalism.