A Note on Mixed Matrix Moments for the Complex Ginibre Ensemble

Abstract

We consider the mixed matrix moments for the complex Ginibre ensemble. These are well-known. We consider the relation to the expected overlap functions of Chalker and Mehlig. This leads to new asymptotic problems for the overlap. We obtain some results, but we also state some remaining open problems.

Final version. 18 pages, 1 figure

References in corpus (4)

• Broken Replica Symmetry Bounds in the Mean Field Spin Glass Model
• Experimental Width Shift Distribution: A Test of Nonorthogonality for Local and Global Perturbations
• Dysonian dynamics of the Ginibre ensemble
• Exact replica treatment of non-Hermitean complex random matrices

Cited by in corpus (13)

• The distribution of overlaps between eigenvectors of Ginibre matrices
• On statistics of bi-orthogonal eigenvectors in real and complex Ginibre ensembles: combining partial Schur decomposition with supersymmetry
• Squared eigenvalue condition numbers and eigenvector correlations from the single ring theorem
• Probing non-orthogonality of eigenvectors in non-Hermitian matrix models: diagrammatic approach
• Condition numbers for real eigenvalues in the real Elliptic Gaussian ensemble
• Fixed points and cycle structure of random permutations
• Non-Hermitian Hamiltonians Violate the Eigenstate Thermalization Hypothesis
• Full Dysonian dynamics of the complex Ginibre ensemble
• Spectra of large time-lagged correlation matrices from Random Matrix Theory
• Eigenfunction non-orthogonality factors and the shape of CPA-like dips in a single-channel reflection from lossy chaotic cavities
• Universal eigenvector correlations in quaternionic Ginibre ensembles
• Pfaffian structure of the eigenvector overlap for the symplectic Ginibre ensemble
• Condition numbers for real eigenvalues of real elliptic ensemble: weak non-normality at the edge