Random Matrix Theory: Invariant Ensembles and Universality

By Percy Deift, Dimitri Gioev. 2009

207 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/6d7816edc973b29b1132e66c79ffd0f4ec534ba8

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Statistics and Probability

Citations in the corpus

Rigidity of eigenvalues of generalized Wigner matrices (2010, unknown): “, [8, 12, 13, 30] and [2, 10, 11] for a review.”
Beta ensembles, stochastic Airy spectrum, and a diffusion (2006, unknown): “For these special values of β, the above model is solvable: all finite-dimensional correlation functions may be computed explicitly in terms of Hermite functions, allowing for a startling collection of precise local limit theorems for the random points (see [7], [8] for background).”
Random matrix theory in statistics: A review (2014, background): “…processes, and the role of the eigenvalue statistics in physics, can be found in the monographs (Akemann et al., 2011; Anderson et al., 2009; Deift, 2000; Deift and Gioev, 2009; Forrester, 2010; Guionnet, 2009; Mehta, 2004; Tao, 2012), and the survey articles (Diaconis, 2003; Soshnikov, 2000).”
Universality of local spectral statistics of random matrices (2011, background): “We refer the reader to recent comprehensive books [14, 16, 1].”
A Dynamical Approach to Random Matrix Theory (2017, background): “, the Gaussian ensembles, can be explicitly expressed in terms of a Fredholm determinant [37,40].”
Spectral statistics of Erdős–Rényi graphs I: Local semicircle law (2011, background): “ty in the interior of the spectrum and the edge universality near the spectral edge. The bulk and edge universalities for invariant ensembles have been extensively studied; see e.g. [2, 6, 7, 27] and [1, 4, 5] for a review. A key fact that attributes to the progress in the study of invariant ensembl”
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.”
Bulk universality for generalized Wigner matrices (2010, unknown): “[3, 6, 7, 8, 9, 25, 26, 27] and references therein).”
Universality for generalized Wigner matrices with Bernoulli distribution (2010, methodology): “The formulas for the GOE cases are more complicated and we refer the reader to standard references such as [1, 6, 20, 24].”
Eigenvector distribution of Wigner matrices (2011, unknown): “…2 01 1 Eigenvector Distribution of Wigner Matrices Antti Knowles1∗ and Jun Yin2† Department of Mathematics, Harvard University Cambridge MA 02138, USA knowles@math.harvard.edu1 jyin@math.harvard.edu2 November 8, 2011 We consider N×N Hermitian or symmetric random matrices with independent entries.”
The local relaxation flow approach to universality of the local statistics for random matrices (2009, background): “, see [7, 8, 9, 10] and references therein, and also by Bleher and Its [5] and Pastur and Schcherbina [32].”
A pedestrian's view on interacting particle systems, KPZ universality and random matrices (2008, background): “Universality results are also available for large classes of matrix ensembles (see [35, 43] and references therein).”
Fixed Energy Universality for Generalized Wigner Matrices (2014, methodology): “First we will need the following precise estimates on the correlation functions of GOE, which were proved in [29, Theorem 3] and [5].”