On the empirical distribution of eigenvalues of large dimensional information-plus-noise-type matrices

By R. Brent Dozier, J. Silverstein. 2007

182 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/bd8169abda9a2ea71da0bf17be516bc611589e47

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Citations in the corpus

ON BILINEAR FORMS BASED ON THE RESOLVENT OF LARGE RANDOM MATRICES (2010, background): “It is of interest to notice that, due to some fortunate cancellation, the particular study of bilinear forms of the type unQn(z)vn or their analogues of the type ũnQ̃n(z)ṽ ∗ n can be circumvented to establish first order results for non-centered random matrices (see for instance [8], [15]).”
Outlier Eigenvalues for Deformed I.I.D. Random Matrices (2014, background): “According to Dozier and Silverstein [26], almost surely the empirical spectral measure µMzNM z N ∗ of M zNM z N ∗ converges weakly towards a nonrandom distribution µz which is characterized in terms of its Stieltjes transform which satisfies the following equation: for any w ∈ C+, gµz(w) = ∫ 1 (1− σ”
Spectrum estimation for large dimensional covariance matrices using random matrix theory (2006, methodology): “For instance, it can be easily adapted to perform a similar estimation procedure in the context investigated in [15].”
Analysis of the limiting spectral distribution of large dimensional information-plus-noise type matrices (2007, methodology): “We begin our analysis by establishing some useful definitions and inequalities that were originally presented in section 4 of Dozier and Silverstein [3].”
On the spectrum of sum and product of non-hermitian random matrices (2010, unknown): “Theorem 7 (Convergence of singular values, [5]).”
A Random Matrix Approach to Neural Networks (2017, background): “Besides, it was shown in (Silverstein and Bai, 1995; Silverstein and Choi, 1995) that the function mµ̄n is well-defined, complex analytic and bounded on all compact subsets of C \ R+.”
Random matrix theory in statistics: A review (2014, background): “Dozier and Silverstein (2007b,a) proved the existence of the limiting ESD of Wn given by (22), and analyzed the behavior of the limit if (7) holds and the ESD of n (1)RnRnn converges to a nonrandom limit distribution on R þ . Hachem et al. (2007) considered a further generalization and derived deter”
Universality and the circular law for sparse random matrices. (2010, methodology): “entries, since there Dozier and Silverstein’s result [7] cannot be applied.”
Random matrices: Universality of ESDs and the circular law (2008, methodology): “1 of [3] which we used in the end of Section 6.”
On the Marchenko-Pastur and Circular Laws for some Classes of Random Matrices with Dependent Entries (2011, methodology): “The proof relies heavily on the Stieltjes transform techniques (motivated by [13]) and will be presented in a separate article.”
Circular law theorem for random Markov matrices (2008, unknown): “5) and the result of Dozier and Silverstein [18] hold.”
Deterministic equivalents for certain functionals of large random matrices (2005, methodology): “MR1422374 [24] Silverstein, J. W. (1995).”
Finite sample approximation results for principal component analysis: a matrix perturbation approach (2009, background): “According to [9, 34] near the boundary b = support(F ), the density F exhibits a behavior closely resembling √ |b− x|.”
Around the circular law (2011, background): “9 appears as a special case of the work of Dozier and Silverstein for information plus noise random matrices [39].”
From the Littlewood-Offord problem to the Circular Law: universality of the spectral distribution of random matrices (2008, methodology): “Using techniques from probability, such as the moment method, one can show that the distributions of the singular values of 1 √ n An − zI and 1 √nBn − zI are asymptotically the same 17 [3, 54, 10, 55, 11].”
Almost sure localization of the eigenvalues in a Gaussian information plus noise model - Application to the spiked models (2010, unknown): “g Dozier-Silverstein [14]).”