# Large deviations from the circular law

Gérard Ben Arous; Ofer Zeitouni

ESAIM: Probability and Statistics (2010)

- Volume: 2, page 123-134
- ISSN: 1292-8100

## Access Full Article

top## Abstract

top## How to cite

topBen Arous, Gérard, and Zeitouni, Ofer. "Large deviations from the circular law." ESAIM: Probability and Statistics 2 (2010): 123-134. <http://eudml.org/doc/197736>.

@article{BenArous2010,

abstract = {
We prove a full large deviations principle, in the scale N2,
for the empirical measure of the eigenvalues of an N x N
(non self-adjoint) matrix composed of i.i.d. zero mean random
variables with variance N-1. The (good) rate function which
governs this rate function possesses as unique minimizer the
circular law, providing an alternative proof of convergence to
the latter. The techniques are related to recent work by Ben
Arous and Guionnet, who treat the self-adjoint case. A crucial
role is played by precise determinant computations due to Edelman
and to Lehmann and Sommers.
},

author = {Ben Arous, Gérard, Zeitouni, Ofer},

journal = {ESAIM: Probability and Statistics},

keywords = {Large deviations / circular law / non commutative entropy.; circular law; large deviations; random matrices},

language = {eng},

month = {3},

pages = {123-134},

publisher = {EDP Sciences},

title = {Large deviations from the circular law},

url = {http://eudml.org/doc/197736},

volume = {2},

year = {2010},

}

TY - JOUR

AU - Ben Arous, Gérard

AU - Zeitouni, Ofer

TI - Large deviations from the circular law

JO - ESAIM: Probability and Statistics

DA - 2010/3//

PB - EDP Sciences

VL - 2

SP - 123

EP - 134

AB -
We prove a full large deviations principle, in the scale N2,
for the empirical measure of the eigenvalues of an N x N
(non self-adjoint) matrix composed of i.i.d. zero mean random
variables with variance N-1. The (good) rate function which
governs this rate function possesses as unique minimizer the
circular law, providing an alternative proof of convergence to
the latter. The techniques are related to recent work by Ben
Arous and Guionnet, who treat the self-adjoint case. A crucial
role is played by precise determinant computations due to Edelman
and to Lehmann and Sommers.

LA - eng

KW - Large deviations / circular law / non commutative entropy.; circular law; large deviations; random matrices

UR - http://eudml.org/doc/197736

ER -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.