Publication : t07/031

Extreme value problems in Random Matrix Theory and other disordered systems

Biroli G. (CEA, DSM, SPhT (Service de Physique Théorique), F-91191 Gif-sur-Yvette, FRANCE)
Bouchaud J.-P. (CEA, IRAMIS, SPEC (Service de Physique de lEtat Condensé), F-91191 Gif-sur-Yvette, FRANCE)
Potters M. (Science & Finance, Capital Fund Management 6 Bld Haussmann, F-75009 Paris, France)
Abstract:
We review some applications of central limit theorems and extreme values statistics in the context of disordered systems. We discuss several problems, in particular concerning Random Matrix Theory and the generalisation of the Tracy-Widom distribution when the disorder has "fat tails". We underline the relevance of power-law tails for Directed Polymers and mean-field Spin Glasses, and we point out various open problems and conjectures on these matters. We find that in many instances the assumption of Gaussian disorder cannot be taken for granted.
Année de publication : 2007
Revue : J. Stat. Mech. P07019 (2007)
DOI : 10.1088/1742-5468/2007/07/P07019
Preprint : arXiv:cond-mat/0702244
Lien : http://www.iop.org/EJ/abstract/-search=29589123.2/1742-5468/2007/07/P07019
Numéro Exterieur : SPEC-S07/006
Langue : Anglais
Editeurs : Evans M.R., Franz S., Godrèche C., Mukamel D.

Fichier(s) à télécharger :
  • 1742-5468_2007_07_P07019.pdf
  • jstat.pdf
  • publi.pdf

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