# Global Poissonian behavior of the eigenvalues and localization centers of random operators in the localized phase

Frédéric Klopp^{[1]}

- [1] LAGA, U.M.R. 7539 C.N.R.S Institut Galilée Université Paris-Nord 99 Avenue J.-B. Clément F-93430 Villetaneuse France

Séminaire Laurent Schwartz — EDP et applications (2011-2012)

- Volume: 2011-2012, page 1-12
- ISSN: 2266-0607

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topKlopp, Frédéric. "Global Poissonian behavior of the eigenvalues and localization centers of random operators in the localized phase." Séminaire Laurent Schwartz — EDP et applications 2011-2012 (2011-2012): 1-12. <http://eudml.org/doc/251174>.

@article{Klopp2011-2012,

abstract = {In the present note, we review some recent results on the spectral statistics of random operators in the localized phase obtained in [12]. For a general class of random operators, we show that the family of the unfolded eigenvalues in the localization region considered jointly with the associated localization centers is asymptotically ergodic. This can be considered as a generalization of [10]. The benefit of the present approach is that one can vary the scaling of the unfolded eigenvalues covariantly with that of the localization centers. The convergence result then holds for all the scales that are asymptotically larger than the localization scale. We also provide a similar result that is localized in energy. Full proofs of the results presented here will be published elsewhere ([12]).},

affiliation = {LAGA, U.M.R. 7539 C.N.R.S Institut Galilée Université Paris-Nord 99 Avenue J.-B. Clément F-93430 Villetaneuse France},

author = {Klopp, Frédéric},

journal = {Séminaire Laurent Schwartz — EDP et applications},

keywords = {random operators; eigenvalues; localization centers},

language = {eng},

pages = {1-12},

publisher = {Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique},

title = {Global Poissonian behavior of the eigenvalues and localization centers of random operators in the localized phase},

url = {http://eudml.org/doc/251174},

volume = {2011-2012},

year = {2011-2012},

}

TY - JOUR

AU - Klopp, Frédéric

TI - Global Poissonian behavior of the eigenvalues and localization centers of random operators in the localized phase

JO - Séminaire Laurent Schwartz — EDP et applications

PY - 2011-2012

PB - Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique

VL - 2011-2012

SP - 1

EP - 12

AB - In the present note, we review some recent results on the spectral statistics of random operators in the localized phase obtained in [12]. For a general class of random operators, we show that the family of the unfolded eigenvalues in the localization region considered jointly with the associated localization centers is asymptotically ergodic. This can be considered as a generalization of [10]. The benefit of the present approach is that one can vary the scaling of the unfolded eigenvalues covariantly with that of the localization centers. The convergence result then holds for all the scales that are asymptotically larger than the localization scale. We also provide a similar result that is localized in energy. Full proofs of the results presented here will be published elsewhere ([12]).

LA - eng

KW - random operators; eigenvalues; localization centers

UR - http://eudml.org/doc/251174

ER -

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