The supersymmetry method of random matrix theory
Martin R. Zirnbauer
TL;DR
This paper reviews the supersymmetry method in random matrix theory, focusing on Hermitian band matrices, and discusses the original and recent variants with an emphasis on mathematical rigor.
Contribution
It provides a detailed review of the supersymmetry method applied to Hermitian band matrices, highlighting the correctness of the mathematical reasoning involved.
Findings
Analysis of the original supersymmetry method by Schaefer and Wegner
Discussion of a recent variant by Fyodorov
Emphasis on mathematical rigor in the method
Abstract
The supersymmetry method pioneered by Wegner and Efetov (1979-1983) is reviewed for the case of Hermitian band random matrices, with special attention given to the original method of Schaefer and Wegner and a recent variant due to Fyodorov. Particular emphasis is placed on correctness of the mathematical reasoning.
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Taxonomy
TopicsRandom Matrices and Applications · Quantum Information and Cryptography · Quantum chaos and dynamical systems