A Fourier view on the R-transform and related asymptotics of spherical integrals

By Alice Guionnet, Mylène Mäıda. 2005

135 citations recorded by the source corpus.

Subfields: Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/bf0c3c38f46629d653ad5153ced2f2fb88c32c8f

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Citations in the corpus

Second order freeness and fluctuations of random matrices. III: Higher order freeness and free cumulants (2006, result): “In a forthcoming work we will investigate the relevance of higher order freeness for Itzykson-Zuber integrals more detailed, in particular, in comparison with and extension of results of Zinn-Justin [ZJ99], Collins [Col03], and Guionnet and Maida [GM05].”
Asymptotics of unitary and orthogonal matrix integrals (2006, background): “In the last two decades it has also become an issue to study its large dimension asymptotics [18, 36, 11, 15].”
The eigenvalues and eigenvectors of finite, low rank perturbations of large random matrices (2009, background): “(such as the ones appearing in [19, 20]) to these implicit master equation representations.”
The Landscape of the Spiked Tensor Model (2017, methodology): “est elements of x;y. If d(0x;0 y) n , jx 1 y 1j, and kxk 1;kyk 1M, then for suciently large n log 1 n I n (;x ) 1 n n y g ;;M : (52) Lemma 8 (Limiting distribution of spherical integral [GM05], Theorem 6). Let >0, fx(n)g n2N+ be a sequence of vectors with empirical measure L n converging weakly ”
Large deviations for the largest eigenvalue of Rademacher matrices (2018, background): “were studied in [15] where it was proved that”
Representations of classical Lie groups and quantized free convolution (2013, methodology): “^ = 2Nfor the symplectic and orthogonal groups. Remark. 1M here and below means the sequence of Mones (1;:::;1 | {z } M ). Pointwise identity (4.6) for the unitary groups and real u irst appeared in [GM]. In [GP] it was extended to complex u iand other classical Lie groups. Note that neither of the ”
Large deviations for the largest eigenvalue of rank one deformations of Gaussian ensembles (2006, background): “According to Theorem 6 of (12), we know that, for some values of θ, the limit of 1 N log I N (θ,BN ) as N goes to infinity depends not only on the limiting spectral measure of BN but also on the limit of λ1(BN ).”
Asymptotic power of sphericity tests for high-dimensional data (2013, background): “Guionnet and Mäıda (2005) study the asymptotic behavior of spherical integrals using large deviation techniques.”
Cleaning large correlation matrices: tools from random matrix theory (2016, background): “Using Dyson’s Brownian motion, one can find [177,178]: Fβ=2(A, B) = limN→∞ N−2 ln I2(A, B): F2(A, B) = − 3 4 − S2(A, B)+ 1 2  dx x(2)(ρA(x)+ ρB(x))− 1 2  dxdy [ρA(x)ρA(y)+ ρB(x)ρB(y)] ln |x− y|,”