Universality for certain hermitian Wigner matrices under weak moment conditions

Kurt Johansson

Annales de l'I.H.P. Probabilités et statistiques (2012)

  • Volume: 48, Issue: 1, page 47-79
  • ISSN: 0246-0203

Abstract

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We study the universality of the local eigenvalue statistics of Gaussian divisible Hermitian Wigner matrices. These random matrices are obtained by adding an independent GUE matrix to an Hermitian random matrix with independent elements, a Wigner matrix. We prove that Tracy–Widom universality holds at the edge in this class of random matrices under the optimal moment condition that there is a uniform bound on the fourth moment of the matrix elements. Furthermore, we show that universality holds in the bulk for Gaussian divisible Wigner matrices if we just assume finite second moments.

How to cite

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Johansson, Kurt. "Universality for certain hermitian Wigner matrices under weak moment conditions." Annales de l'I.H.P. Probabilités et statistiques 48.1 (2012): 47-79. <http://eudml.org/doc/272083>.

@article{Johansson2012,
abstract = {We study the universality of the local eigenvalue statistics of Gaussian divisible Hermitian Wigner matrices. These random matrices are obtained by adding an independent GUE matrix to an Hermitian random matrix with independent elements, a Wigner matrix. We prove that Tracy–Widom universality holds at the edge in this class of random matrices under the optimal moment condition that there is a uniform bound on the fourth moment of the matrix elements. Furthermore, we show that universality holds in the bulk for Gaussian divisible Wigner matrices if we just assume finite second moments.},
author = {Johansson, Kurt},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {Wigner matrix; gaussian divisible; optimal moment condition; universality; Tracy–Widom distribution; Gaussian divisible; Tracy-Widom distribution},
language = {eng},
number = {1},
pages = {47-79},
publisher = {Gauthier-Villars},
title = {Universality for certain hermitian Wigner matrices under weak moment conditions},
url = {http://eudml.org/doc/272083},
volume = {48},
year = {2012},
}

TY - JOUR
AU - Johansson, Kurt
TI - Universality for certain hermitian Wigner matrices under weak moment conditions
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2012
PB - Gauthier-Villars
VL - 48
IS - 1
SP - 47
EP - 79
AB - We study the universality of the local eigenvalue statistics of Gaussian divisible Hermitian Wigner matrices. These random matrices are obtained by adding an independent GUE matrix to an Hermitian random matrix with independent elements, a Wigner matrix. We prove that Tracy–Widom universality holds at the edge in this class of random matrices under the optimal moment condition that there is a uniform bound on the fourth moment of the matrix elements. Furthermore, we show that universality holds in the bulk for Gaussian divisible Wigner matrices if we just assume finite second moments.
LA - eng
KW - Wigner matrix; gaussian divisible; optimal moment condition; universality; Tracy–Widom distribution; Gaussian divisible; Tracy-Widom distribution
UR - http://eudml.org/doc/272083
ER -

References

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