Large deviations from the circular law

Gérard Ben Arous; Ofer Zeitouni

ESAIM: Probability and Statistics (2010)

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

Abstract

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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.

How to cite

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Ben 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 -

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