Analysis of the limiting spectral distribution of large dimensional information-plus-noise type matrices

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Spectrum of Non-Hermitian Heavy Tailed Random Matrices (2010, background): “Following Dozier and Silverstein [16, 15], if F has finite positive variance σ2, then for every z ∈ C, there exists a probability measure Qσ,z on [0,∞) depending only on σ and z, with explicit Cauchy-Stieltjes transform, such that a.s. (almost surely) ν 1√ n X−zI n→∞ Qσ,z (1.1) where denotes the wea”
Analysis of the limiting spectral measure of large random matrices of the separable covariance type (2013, methodology): “Parallelling the assumptions made in [15], [20] and [5], we restrict ourselves to the case where a = xI,Ĩ(δ̃a) for some δ̃a ∈ dom(xI,Ĩ).”
Outlier Eigenvalues for Deformed I.I.D. Random Matrices (2014, methodology): “The characterization of the complement in R \ {0} of the support of μz established in [25] and Proposition 2.”
Almost sure localization of the eigenvalues in a Gaussian information plus noise model - Application to the spiked models (2010, background): “It is shown in [13] that Re(1+σ(2)cN mN (z)) = 1+σ(2)(1− cN )G(z)+ Im(1+σ(2)cN mN (z))z2G(z) 1− g (z)+ z1G(z) , for z ∈C+.”