Convergence rate of expected spectral distributions of large random matrices
By Z. Bai. 2008
96 citations recorded by the source corpus.
View Paper: https://www.semanticscholar.org/paper/7c97c938deaf93ececd7ff9c46d4cc7498e1580b
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
Citations in the corpus
- ASYMPTOTICS OF SAMPLE EIGENSTRUCTURE FOR A LARGE DIMENSIONAL SPIKED COVARIANCE MODEL (2007, methodology): “Bai (1993) proved under fairly weak conditions (Bai (1993, Thm. 3.2), that if θ1 ≤ p/n ≤ θ2 where 0 θ1 1 θ2 ∞, then ‖Fn,p − F p n ‖∞ ≤ C1(θ1, θ2)n− 5 48 , (62) where Fp/n denotes the Marčenko-Pastur law with parameter p/n.”
- Sparse regular random graphs: Spectral density and eigenvectors (2009, background): “In the last couple of decades there has been an enormous amount of activity in the study of universal properties of random matrices, inspired by their connection to (universal) physical systems.”
- Cleaning large correlation matrices: tools from random matrix theory (2016, background): “In fact, one can rigorously estimate the expected difference between the ESD at finite N and the asymptotic LSD for N = ∞, which vanishes as N−1/4 as soon as the Mij’s have a finite fourth moment, and as N−2/5 if all the moments of the Mij are finite (see [76]).”
- LARGE SAMPLE COVARIANCE MATRICES WITHOUT INDEPENDENCE STRUCTURES IN COLUMNS (2008, background): “where, in accordance with Bai (1993), the square root of a complex number is defined to be the one with a positive imaginary part.”
- Large deviations for the largest eigenvalue of rank one deformations of Gaussian ensembles (2006, background): “We know from the result of Bai in (1) that ‖EN−1 N FN−1 − Fβ‖ = O(N− 1 4 ), where EN−1 N is the expectation under P N−1 N , so that PN−1 N (‖FN−1 − Fβ‖∞ > N−κ) 6 PN−1 N ( ‖FN−1 − EN−1 N FN−1‖∞ > N−κ 2 )”