Asymptotic freeness by generalized moments for Gaussian and Wishart matrices. Application to beta random matrices

By M. Casalis, M. Capitaine. 2004

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Annular noncrossing permutations and partitions, and second-order asymptotics for random matrices (2003, background): “(For a recent discussion of this, see [5].”
GLOBAL FLUCTUATIONS FOR LINEAR STATISTICS OF β-JACOBI ENSEMBLES (2012, methodology): “Other approaches to calculating fluctuations for linear functionals for β-ensembles include the Capitaine and Casalis work [12], which, through free probability, obtains results for both Wishart and Jacobi (Double Wishart) matrices in the case β = 2.”
Approximation of Haar distributed matrices and limiting distributions of eigenvalues of Jacobi ensembles (2009, background): “distribution. The exact limiting distribution for complex case was given explicitly in [ 14 ], see also”
Asymptotic behavior of random determinants in the Laguerre, Gram and Jacobi ensembles (2006, background): “Capitaine and Casalis [11] studied the complex case in the asymptotical regime n1/r → u′, n2/r → v′ with u′ + v′ ≥ 1.”
Second order freeness and fluctuations of random matrices: I. Gaussian and Wishart matrices and cyclic Fock spaces (2004, background): “Our more general version follows by the same kind of calculations (c.f. Capitaine and Casalis [ CC , §5]).”
The singular values and vectors of low rank perturbations of large rectangular random matrices (2011, background): “Examples of random matrices satisfying this hypothesis can be found in e.g. [5, 19, 6, 11, 3, 45].”