PATTERNS IN EIGENVALUES: THE 70TH JOSIAH WILLARD GIBBS LECTURE

By Neil O'Connell. 2003

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Determinantal Point Processes for Machine Learning (2012, background): “In fact, years before Macchi gave them a general treatment, specific DPPs appeared in major results in random matrix theory [Mehta and Gaudin, 1960, Dyson, 1962a,b,c, Ginibre, 1965], where they continue to play an important role [Diaconis, 2003, Johansson, 2005b].”
Approximation of Haar distributed matrices and limiting distributions of eigenvalues of Jacobi ensembles (2009, background): “Diaconis[21], Eaton[27] and Muirhead[57] for the interest of statistics.”
Random matrix theory in statistics: A review (2014, background): “, 2009; Deift, 2000; Deift and Gioev, 2009; Forrester, 2010; Guionnet, 2009; Mehta, 2004; Tao, 2012), and the survey articles (Diaconis, 2003; Soshnikov, 2000).”
High Dimensional Statistical Inference and Random Matrices (2006, background): “Other overviews with substantial statistical content include [5], [30] and [36].”
Determinantal Processes and Independence (2005, background): “Determinantal processes arise naturally in several other settings, including eigenvalues of random matrices, random spanning trees and nonintersecting paths; see, e.g., Burton and Pemantle [4], Soshnikov [27], Lyons [20], Lyons and Steif [21], Shirai and Takahashi [25], Johansson [14], Borodin, Okou”
Second order freeness and fluctuations of random matrices. III: Higher order freeness and free cumulants (2006, background): “Global fluctuations of the eigenvalues (that is, linear functionals of the eigenvalues) of random matrices have been widely investigated in the last decade; see, e.g., [Joh98, Dia03 , Rad04, MN04, M´SS04].”
How many entries of a typical orthogonal matrix can be approximated by independent normals (2006, background): “3 from [10] is as follows: what are the largest orders of pn and qn such that the variation distance between the joint distribution of the entries of Zn and that of pnqn independent standard normals goes to zero as n → ∞.”
Zeros of Gaussian Analytic Functions and Determinantal Point Processes (2009, background): “There is a long history going back to Maxwell (see (18) and references therein).”
COMBINATORIAL ASPECTS OF CONNES'S EMBEDDING CONJECTURE AND ASYMPTOTIC DISTRIBUTION OF TRACES OF PRODUCTS OF UNITARIES (2004, background): “As in [4] this means that the asymptotic distri but on of the variablesTr(W1), .”
Lectures on the Combinatorics of Free Probability (2006, background): “For more information and references about Haar unitary random matrices, we refer to [23, 29, 34].”
Determinantal probability measures (2002, background): “Essentially the same observation is made by Dubhashi and Ranjan (1998). The standard proof, with the addition of (6.”