Fetching the paper…

Reading the bibliography…

2014

Anisotropic local laws for random matrices

Knowles, Antti, Yin, Jun

Original
PDF
Post on X

Understand

We develop a new method for deriving local laws for a large class of random matrices.

It is applicable to many matrix models built from sums and products of deterministic or independent random matrices.
In particular, it may be used to obtain local laws for matrix ensembles that are \emph{anisotropic} in the sense that their resolvents are well approximated by deterministic matrices that are not multiples of the identity.
For definiteness, we present the method for sample covariance matrices of the form $Q := T X X^* T^*$, where $T$ is deterministic and $X$ is random with independent entries.

Anisotropic local laws for random matrices · Around

Built on

L. Erdős, A. Knowles, and H.-T. Yau,
1926
Earlier work this paper cites.
E.P. Wigner,
1955
Earlier work this paper cites.
V. A. Marchenko and L. A. Pastur,
1967
Earlier work this paper cites.
L. A. Pastur,
1972
Earlier work this paper cites.
C. Tracy and H. Widom,
1994
Earlier work this paper cites.
J. W. Silverstein and Z. Bai,
1995
Earlier work this paper cites.
J. W. Silverstein and S.-I. Choi,
1995
Earlier work this paper cites.
Z. Bai and J. W. Silverstein,
1998
Earlier work this paper cites.
N. El Karoui,
2007
Earlier work this paper cites.
K. Johansson,
2007
Earlier work this paper cites.

Similar

A. Onatski,
2008
Cited alongside, same era.
L. Erdős, B. Schlein, and H.-T. Yau,
2009
Cited alongside, same era.
A. Lytova and L. Pastur,
2009
Cited alongside, same era.
T. Shcherbina,
2009
Cited alongside, same era.
Z. Bai and J. W. Silverstein,
2010
Cited alongside, same era.
T. Tao and V. Vu,
2011
Cited alongside, same era.
L. Erdős, A. Knowles, H.-T. Yau, and J. Yin,
2012
Cited alongside, same era.
L. Erdős, B. Schlein, H.-T. Yau, and J. Yin,

Then

W. Hachem, P. Loubaton, J. Najim, and P. Vallet,
2013
Later among the works it cites.
A. Knowles and J. Yin,
2013
Later among the works it cites.
A. Bloemendal, L. Erdős, A. Knowles, H.-T. Yau, and J. Yin,
2014
Closest in time.
N. S. Pillai and J. Yin,
2014
Closest in time.
V. Kargin,
2015
Closest in time.
J. O. Lee and K. Schnelli,
2015
Closest in time.
A. Bloemendal, A. Knowles, H.-T. Yau, and J. Yin,
2016
Closest in time.
M. Capitaine and S. Péché,

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

2012

Cited alongside, same era.

L. Erdős, H.-T. Yau, and J. Yin,

2012

Cited alongside, same era.

Z. Bao, L. Erdős, and K. Schnelli,

Cited in the paper.

Z. Bao, G. Pan, and W. Zhou,

Cited in the paper.

F. Benaych-Georges,

Cited in the paper.

2016

Closest in time.

S. Chatterjee,

2076

Closest in time.