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Stochastic Processes and Random MatricesLecture Notes of the Les Houches Summer School: Volume 104, July 2015$
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Grégory Schehr, Alexander Altland, Yan V. Fyodorov, Neil O'Connell, and Leticia F. Cugliandolo

Print publication date: 2017

Print ISBN-13: 9780198797319

Published to Oxford Scholarship Online: January 2018

DOI: 10.1093/oso/9780198797319.001.0001

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Random matrix theory and quantum chromodynamics

Random matrix theory and quantum chromodynamics

(p.228) 5 Random matrix theory and quantum chromodynamics
Stochastic Processes and Random Matrices

Gernot Akemann

Oxford University Press

This chapter was originally presented to a mixed audience of physicists and mathematicians with some basic working knowledge of random matrix theory. The first part is devoted to the solution of the chiral Gaussian unitary ensemble in the presence of characteristic polynomials, using orthogonal polynomial techniques. This includes all eigenvalue density correlation functions, smallest eigenvalue distributions, and their microscopic limit at the origin. These quantities are relevant for the description of the Dirac operator spectrum in quantum chromodynamics with three colors in four Euclidean space-time dimensions. In the second part these two theories are related based on symmetries, and the random matrix approximation is explained. In the last part recent developments are covered, including the effect of finite chemical potential and finite space-time lattice spacing, and their corresponding orthogonal polynomials. This chapter also provides some open random matrix problems.

Keywords:   random matrix theory, chiral ensembles, Laguerre–Wishart ensembles, orthogonal polynomials, quantum chromodynamics

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