Spectral Analysis of Large Dimensional Random Matrices

By Z. Bai, J. Silverstein. 2009

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Citations in the corpus

High-dimensional dynamics of generalization error in neural networks (2017, background): “and Solla, 1991; Seung, Sompolinsky, and Tishby, 1992; Dodier, 1995; P.F. Baldi and Hornik, 1995; Kinouchi and Caticha, 1995; Dunmur and Wallace, 1999; Krogh and Hertz, 1992; Hoyle and Rattray, 2007; Bai and Silverstein, 2010; Benaych-Georges and Rao, 2011; Benaych-Georges and Rao, 2012). Our result”
Introduction to the non-asymptotic analysis of random matrices (2010, background): “The books [51, 5, 23, 6] offer thorough introduction to the classical problems of random matrix theory and its fascinating connections.”
The LASSO Risk for Gaussian Matrices (2010, neutral): “A very general result was proved in [6] (see also [4]).”
Another look at the moment method for large dimensional random matrices (2008, methodology): “ν with variance 1 then W continues to be the LSD (see Bai and Silverstein, 2006) [3].”
Analytic subordination theory of operator-valued free additive convolution and the solution of a general random matrix problem (2013, methodology): “In the random matrix context, Problem 2 was addressed for various polynomials - and usually, also for specific choices of the distributions of the X (N) i - in work of: Marchenko-Pastur [25], Girko [19], Bai and Silverstein [13]; Tulino and Verdu [37]; Müller [27]; Moustakis and Simon [26]; Hechem,”
Random matrices: Universal properties of eigenvectors (2011, methodology): “11|u 1|≤A ≥ sup K EG21 |G|≤K = 1. We conclude that nEu2 1,≤ = 1−o(1) and nEu2 1,> = o(1) and Claim 2 follows. Now we turn to Claim 1. Here we use the moment method. By Carleman’s theorem (see e.g. [1]), it suﬃces to show that for each ﬁxed positive integer k, nk/2E(a· u ≤) k = EGk +o(1). The left”
Singular vector and singular subspace distribution for the matrix denoising model (2018, background): “Furthermore, one can easily check that m1(z) and m2(z) satisfy the following self-consistent equations (see [2] for instance)”
Alternative asymptotics for cointegration tests in large VARs (2016, background): “Then, by Theorem A45 (norm inequality) of Bai and Silverstein (2010), L ( Fp,Tγ , FSR ) ≤ ‖S‖ ≤ K√γ, whereas by their Theorem A43 (rank inequality), L (FSR, Fp,T∞) ≤ 1 p rankR ≤ τ.”
Random matrices: Sharp concentration of eigenvalues (2012, methodology): “See for instance [4] for a proof of this theorem and for historical background.”
The spectral norm of random inner-product kernel matrices (2015, background): “t;0, MP;shift has Stieltjes transform m MP;shift(z) = z a + q z a 2 4 2 (z+ a) : Here, the branch of the square-root function is chosen to have positive imaginary part. (See Lemmas 2.11 and 3.11 of [2].) The rst equation implies 1 msc(z) = z+ ( a2)m sc(z). When a= 0, this is precisely eq. (1) denin”