2013/07/06 by James A. Mingo, Roland Speicher, Mingo, James A. +1 · 1 citation
Mathematics · #46L54 #60B20 #FOS: Mathematics #Operator Algebras (math.OA) #Probability (math.PR) #math.OA #math.PR #msc:46L54 #msc:60B20
paper · pdf · doi:10.48550/arxiv.1307.1806
arxiv created 2013/07/06 · arxiv updated 2013/07/09
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.