Linear functionals of eigenvalues of random matrices

By Persi Diaconis, Steven N. Evans. 2000

262 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/a466fcf175e3645b5815dd07e64d25d3aa0a22f6

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In Algebra and Number Theory

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In Statistics and Probability

Citations in the corpus

Traces of high powers of the Frobenius class in the hyperelliptic ensemble (2008, unknown): “3) 〈 tr ΘQ trΘ n Q 〉 ∼    ηmηn + 1 q−1 , m + n = 2g ηmηn − ηm+n + ηm 1 q−1 , n = 2g − q q−1 ηm+n, n − m = 2g The expected values for the symplectic group are [5, 4, 8, 12]: i) If m = n then”
Monte Carlo with determinantal point processes (2016, unknown): “See for instance [Johansson, 1997, 1998, Diaconis and Evans, 2001, Soshnikov, 2002, Pastur, 2006, Rider and Virág, 2007, Popescu, 2009, Kriecherbauer and Shcherbina, 2010, Ameur et al., 2011, 2015, Berman, 2012, Shcherbina, 2013, Breuer and Duits, 2013, 2014, Johansson and Lambert, 2015, Lambert,…”
Zeros of Gaussian Analytic Functions and Determinantal Point Processes (2009, background): “A special case in the unit disk (L = 2) was found by Diaconis and Evans (18) as the limit of the logarithmic derivative of characteristic polynomials of random unitary matrices.”
CENTRAL LIMIT THEOREM FOR LINEAR EIGENVALUE STATISTICS OF RANDOM MATRICES WITH INDEPENDENT ENTRIES (2008, background): “In the last decade a number of results on the CLT for linear eigenvalue statistics of various classes of random matrices has been obtained (see [2, 5, 7, 8, 10, 11, 13, 15, 16, 17, 18, 28, 29, 30] and [31] and the references therein).”
Random matrix theory in statistics: A review (2014, result): “Unfortunately, that this is not possible in general follows from the results by Bai and Silverstein (2004) for Wishart matrices and those by Diaconis and Evans (2001) for Haar matrices.”
Maximum of the Characteristic Polynomial of Random Unitary Matrices (2015, background): “Though the traces of powers of UN are not independent, it was shown in [29,30] that they are uncorrelated E ( TrUjN TrU k N ) = δkj min(k,N), (1.”
PATTERNS IN EIGENVALUES: THE 70TH JOSIAH WILLARD GIBBS LECTURE (2003, methodology): “I thank my coauthors—Dan Bump, Steve Evans and Mehrdad Shahshahani— along with my students—Joe Blitzstein, Marc Coram, Jason Fulman, Eric Rains and Kelly Wieand—for their contributions to this work.”
Patterns in eigenvalues: the 70th Josiah Willard Gibbs lecture (2003, methodology): “As discussed in Diaconis-Evans [ 33 ], [35], the Hilbert space H”
Gaussian fluctuations for non-Hermitian random matrix ensembles (2005, unknown): “The Annals of Probability 2006, Vol. 34, No. 6, 2118–2143 DOI: 10.1214/009117906000000403 © Institute of Mathematical Statistics, 2006”
The Noise in the Circular Law and the Gaussian Free Field (2006, methodology): “The proof is largely inspired by the ideas of Diaconis-Evans [6] where the analogous moment formula is established for the eigenvalues of the Haar distributed unitary group.”
Fluctuations of eigenvalues and second order Poincaré inequalities (2007, background): “However, as shown in [20, 21], strikingly exact computations are possible in this case by invoking some deep connections between symmetric function theory and the unitary group.”
Eigenvalue distributions of random unitary matrices (2002, methodology): “Theorem 1. Soshnikov [28] has discussed the multiple interval case using the approach of [9], and Diaconis and Evans [ 10 ] have found a proof of Theorem 1 using methods introduced in [11] studying traces of powers of random unitary matrices.”
How many entries of a typical orthogonal matrix can be approximated by independent normals (2006, background): “Diaconis and Shahshahani [12], Diaconis and Evans [13] and Rains [28] characterized relationships between the traces of n and those of ′n in terms of expectations; Johansson [20] obtained the speed of convergence of traces of n to a normal random variable; D’Aristotile, Diaconis and Newman [8] showe”