An Introduction to Random Matrices

By Greg W. Anderson, Alice Guionnet, Ofer Zeitouni. 2009

400 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/b78c142a5c26781d4be90b0158ef489e2aac429a

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Citations in the corpus

Surprises in High-Dimensional Ridgeless Least Squares Interpolation (2019, unknown): “Properties (a)-(c) are then standard consequences of m1,n being a Stieltjes transform (see, for instance, Anderson et al. (2009)) Lemma 8.”
The Generalization Error of Random Features Regression: Precise Asymptotics and the Double Descent Curve (2019, methodology): “[AGZ09] Greg W.”
Interlacing Families I: Bipartite Ramanujan Graphs of All Degrees (2013, methodology): “This latter technique is inspired by ideas in Free Probability theory [15], [18], an area that originally grew out of operator algebras but which has a number of applications to asymptotic random matrix theory [1].”
The single ring theorem (2009, unknown): “) and (5). Therefore, since Gz n is the Stieltjes transform of E[νzn], by Lemma 13, for any y >0, E[νz n((−y,y))]≤E[νzn((−y∨n−c1,y∨n−c1))]≤ 2c2y∨n−c1 . Thus, we get that for any z ∈ BR and with α∈ [1,2], E[ Zε n−δ (|logx|)αdνz n(x)] ≤ E[ Zn−c1∨δ n−δ (|logx|)αdνz n(x)+ Zε n−c1∨δ (|logx|)αdνz n(x)]”
Large deviations of the extreme eigenvalues of random deformations of matrices (2010, background): “1 Note that in the published version of [1], part i i i) was not mentioned but it appears in the errata sheet available online: http://www.”
Matrix estimation by Universal Singular Value Thresholding (2012, background): “ It may also be derived as a consequence of Wielandt’s minimax principle [14], Section III.3, or Lidskii’s theorem [14], Exercise III.4.3. The case p=2 is sometimes called the Hoﬀman–Wielandt theorem [8], Lemma 2.1.19 and Remark 2.1.20, and the inequality involving the maximum is sometimes called We”
THE SPECTRUM OF RANDOM INNER-PRODUCT KERNEL MATRICES (2012, methodology): “We refer the reader to [2], [18] and [4, Chapters 1-3] for an introduction of these topics.”
The Crystallization Conjecture: A Review (2015, methodology): “e eigenvalues is given by the measure σ solution to the minimization problem in (41). The next order is more complex and its link with the crystal problem is less clear [72]. We refer for instance to [174, 92, 13] for a detailed study of the subject. 3.2. Several types of particles. In order to deal”
Random matrices: tail bounds for gaps between eigenvalues (2015, background): “orem 2.1. To start, let B be the event that the spectrum of X nbelongs to a controlled interval, B= f!: 1(X n);:::; n(X n) ˆ[ 10 p n;10 p n]g: (3) Standard results in random matrix theory (such as [1],[25]) shows that Bholds with probability 1 exp( ( n)). Now let 1 in 1, and consider the event E it”
On the spectral norm of Gaussian random matrices (2015, methodology): “If the variances of the entries are all of the same order, this model is known as a Wigner matrix and has been widely studied in the literature (e.g., [1]).”