Schwinger-Dyson equations: classical and quantum
Operator Algebras
2013-07-09 v1 Probability
Abstract
In this note we want to have another look on Schwinger-Dyson equations for the eigenvalue distributions and the fluctuations of classical unitarily invariant random matrix models. We are exclusively dealing with one-matrix models, for which the situation is quite well understood. Our point is not to add any new results to this, but to have a more algebraic point of view on these results and to understand from this perspective the universality results for fluctuations of these random matrices. We will also consider corresponding non-commutative or "quantum" random matrix models and contrast the results for fluctuations and Schwinger-Dyson equations in the quantum case with the findings from the classical case.
Cite
@article{arxiv.1307.1806,
title = {Schwinger-Dyson equations: classical and quantum},
author = {James A. Mingo and Roland Speicher},
journal= {arXiv preprint arXiv:1307.1806},
year = {2013}
}