Topics in Random Matrix Theory

By Terence Tao. 2012

1,097 citations recorded by the source corpus.

Subfields: Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/fc930ea96445f010b8ba33ad81b4e2223c4bdabe

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In Statistics and Probability

Citations in the corpus

Principal Component Analysis of High-Frequency Data (2016, background): “An important result establishing the continuity of λ is (see, e.g., Tao 2012): Lemma 1. λ : M+d → R̄+d is Lipschitz.”
In-N-Out: Pre-Training and Self-Training using Auxiliary Information for Out-of-Distribution Robustness (2020, background): “7 in Tao [45]), the high level idea is to show that with probability 1−δ each column of the random matrix has a (not too small) component orthogonal to all other columns.”
The Effect of Gradient Noise on the Energy Landscape of Deep Networks (2015, background): “Please refer to, for instance, Mehta (2004) or Tao (2012) for an elaborate exposition.”
Nearly optimal central limit theorem and bootstrap approximations in high dimensions (2020, background): “(logd)4 log(dn) n 1/2 + (logd)7 log(dn) n 1/2 ! logn, (1.4) which nearly matches the dependence on nin the classical Berry-Esseen bound for the one-dimensional (d= 1) case, e.g. Theorem 2.2.15 in [39], but does not provide optimal dependence on Bn= Bn(d) and logd. NEARLY OPTIMAL HIGH-DIMENSIONAL CL”
The Church of the Symmetric Subspace (2013, methodology): “We remark that these techniques have some signiﬁcant overlap with the classic method of moments from random matrix theory (see [34, 3] for reviews, or [2] for a quantum example).”
The spectral norm of random inner-product kernel matrices (2015, neutral): “5 of [29], there exist positive constants A and B such that for all t ≥ A, P[‖W‖ > t√p] ≤ Ae−Btp.”
Neural Empirical Bayes (2019, background): “…an even deeper phenomenon, the concentration of measure, captured by a non-asymptotic result for the deviation of the norm X from √ d , where the deviation has a sub-gaussian tail (Tao, 2012; Vershynin, 2018): A related result states that In above expressions, C and c are absolute constants.”
Cleaning large correlation matrices: tools from random matrix theory (2016, methodology): “Again, we emphasize that this presentation is not intended to be rigorous in a mathematical sense, and we refer to standard RMT textbooks such as [49, 52, 53, 56] for more details.”
Online Factorization and Partition of Complex Networks From Random Walks (2017, neutral): “[27]), we obtain the value of ∑ i>r γ̃ 2 i (0) = poly(m) with probability close to 1 whenm is large.”