Deviation Inequalities on Largest Eigenvalues

By Michel Ledoux. 2007

87 citations recorded by the source corpus.

Subfields: Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/ff8a85d48c8ea212eb1fe780a24061eb172ff0cc

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In Mathematical Physics

In Statistics and Probability

Citations in the corpus

Sure independence screening for ultrahigh dimensional feature space (2006, background): “P (M∗ ⊂ Mγ) = 1 − O(kexp(−Cn 1−2κ /log n)). ( 43 )”
Smallest singular value of a random rectangular matrix (2009, background): “4), which would hold for arbitrary fixed dimensions N and n; see the survey [14] on the largest singular value, and the discussion below on the smallest singular value.”
SPECTRAL DISTRIBUTIONS OF ADJACENCY AND LAPLACIAN MATRICES OF RANDOM GRAPHS (2010, background): “ere is a large deviation inequality P(|n−1/2λ max − √ 2|≥ε)≤e−nCε for any ε>0 as n is suﬃciently SPECTRAL OF LAPLACIAN MATRICES 5 large, where Cε >0 is some constant (see (1.24) and (1.25) from [36] or [8]). With or without the independence assumption, this inequality implies from the Borel–Ca”
The smallest singular value of a random rectangular matrix (2008, background): “4), which would hold for arbitrary fixed dimensions N and n; see the survey [13] on the largest singular value, and the discussion below on the smallest singular value.”
A Selective Overview of Variable Selection in High Dimensional Feature Space (2009, background): “For studies on the extreme eigenvalues and limiting spectral distributions of large random matrices, see, e.g., Silverstein (1985), Bai and Yin (1993), Bai (1999), Johnstone (2001), and Ledoux (2001, 2005).”
Small deviations for beta ensembles (2009, background): “As discussed in [14, 15], the right-tail inequality for the GUE (as well as for the Laguerre Unitary Ensemble, again see below) may be shown to follow from results of Johansson [11] for a more general invariant model related to the geometric distribution that uses large deviation asymptotics and sub”