Complete diagrammatics of the single ring theorem

Abstract

Using diagrammatic techniques, we provide explicit functional relations between the cumulant generating functions for the biunitarily invariant ensembles in the limit of large size of matrices. The formalism allows to map two distinct areas of free random variables: Hermitian positive definite operators and non-normal R-diagonal operators. We also rederive the Haagerup-Larsen theorem and show how its recent extension to the eigenvector correlation function appears naturally within this approach.

18 pages, 6 figures, version accepted for publication

References in corpus (6)

• Eigenvalue distributions of large Euclidean random matrices for waves in random media
• Raney distributions and random matrix theory
• Squared eigenvalue condition numbers and eigenvector correlations from the single ring theorem
• What drives transient behaviour in complex systems?
• Spectra of large time-lagged correlation matrices from Random Matrix Theory
• Spectral density of generalized Wishart matrices and free multiplicative convolution

Cited by in corpus (5)

• Spectral transitions and universal steady states in random Kraus maps and circuits
• Probing non-orthogonality of eigenvectors in non-Hermitian matrix models: diagrammatic approach
• Full Dysonian dynamics of the complex Ginibre ensemble
• Eikonal formulation of large dynamical random matrix models
• On a Generalisation of the Marcenko-Pastur Problem