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A recent line of work has studied the relationship between the Wishart matrix $X^\top X$, where $X\in \mathbb{R}^{d\times n}$ has i.i.d.
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Persi Diaconis and David Freedman. Asymptotics of graphical projection pursuit. The Annals of Statistics
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Persi Diaconis and David Freedman. A dozen de Finetti-style results in search of a theory. Annales de l’Institut Henri Poincaré Probabilités et statistiques
1987
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Persi Diaconis, Morris L. Eaton, and Steffen L. Lauritzen. Finite de Finetti theorems in linear models and multivariate analysis. Scandinavian Journal of Statistics
1992
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1997
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Alison L. Gibbs and Francis E. Su. On choosing and bounding probability metrics. International Statistical Review
2002
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Svante Janson and Andrzej Ruciński. The infamous upper tail. Random Structures Algorithms
2002
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Van H. Vu. Concentration of non-Lipschitz functions and applications. Random Structures Algorithms
2002
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Assaf Naor and Dan Romik. Projecting the surface measure of the sphere of ℓ p n \ell_{p}^{n} . Annales de l’Institut Henri Poincaré Probabilités et statistiques
2003
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Tiefeng Jiang. How many entries of a typical orthogonal matrix can be approximated by independent normals? Annals of Probability
2006
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Sourav Chatterjee and Elizabeth Meckes. Multivariate normal approximation using exchangeable pairs. ALEA Latin American Journal of Probability and Mathematical Statistics
2008
Earlier work this paper cites.
Robb J. Muirhead. Aspects of multivariate statistical theory
2009
Cited alongside, same era.
Luc Devroye, András György, Gábor Lugosi, and Frederic Udina. High-dimensional random geometric graphs and their clique number. Electronic Journal of Probability
2011
Cited alongside, same era.
Sourav Chatterjee. The missing log in large deviations for triangle counts. Random Structures Algorithms
2012
Cited alongside, same era.
Bobby DeMarco and Jeff Kahn. Upper tails for triangles. Random Structures Algorithms
2012
Cited alongside, same era.
Roman Vershynin. Introduction to the non-asymptotic analysis of random matrices
2012
Cited alongside, same era.
Scott Aaronson and Alex Arkhipov. The computational complexity of linear optics. Theory of Computing
Sébastien Bubeck and Shirshendu Ganguly. Entropic CLT and phase transition in high-dimensional Wishart matrices. International Mathematics Research Notices
2016
Later among the works it cites.
Eric Price, Zhao Song, and David P. Woodruff. Fast regression with an ℓ ∞ \ell_{\infty} guarantee. In International Colloquium on Automata, Languages, and Programming (ICALP)
2017
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Anthony Leverrier. SU ( p , q ) \mathrm{SU}(p,q) coherent states and a Gaussian de Finetti theorem. Journal of Mathematical Physics
2018
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2018
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Didier Chételat and Martin T Wells. The middle-scale asymptotics of Wishart matrices. The Annals of Statistics
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2013
Cited alongside, same era.
Scott Aaronson and Alex Arkhipov. Bosonsampling is far from uniform. Quantum Information & Computation
2014
Cited alongside, same era.
Yi Li, Huy L. Nguyen, and David P. Woodruff. On sketching matrix norms and the top singular vector. In ACM-SIAM Symposium on Discrete Algorithms (SODA)
2014
Cited alongside, same era.
Ryan O’Donnell. Analysis of Boolean functions
2014
Cited alongside, same era.
Tiefeng Jiang and Danning Li. Approximation of rectangular beta-Laguerre ensembles and large deviations. Journal of Theoretical Probability
2015
Cited alongside, same era.
Sébastien Bubeck, Jian Ding, Ronen Eldan, and Miklós Z. Rácz. Testing for high-dimensional geometry in random graphs. Random Structures & Algorithms
2016
Cited alongside, same era.
Cited in the paper.
2019
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Tiefeng Jiang and Yutao Ma. Distances between random orthogonal matrices and independent normals. Transactions of the American Mathematical Society
2019
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Miklós Z. Rácz and Jacob Richey. A smooth transition from Wishart to GOE. Journal of Theoretical Probability
2019
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Matthew Brennan, Guy Bresler, and Dheeraj Nagaraj. Phase transitions for detecting latent geometry in random graphs. Probability Theory and Related Fields
2020
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Sébastien Bubeck. Personal communication
2020
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2020
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Kathryn Stewart. Total variation approximation of random orthogonal matrices by Gaussian matrices. Journal of Theoretical Probability
2020
Later among the works it cites.