Publication : t10/166

Tracy-Widom GUE law and symplectic invariants

Borot G. (CEA, IPhT (Institut de Physique Théorique), F-91191 Gif-sur-Yvette, France)
Eynard B. (CEA, IPhT (Institut de Physique Théorique), F-91191 Gif-sur-Yvette, France)
Abstract:
We establish the relation between two objects: an integrable system related to Painleve II equation, and the symplectic invariants of a certain plane curve \Sigma_{TW} describing the average eigenvalue density of a random hermitian matrix spectrum near a hard edge (a bound for its maximal eigenvalue). This explains directly how the Tracy-Widow law F_{GUE}, governing the distribution of the maximal eigenvalue in hermitian random matrices, can also be recovered from symplectic invariants.
Année de publication : 2010
Preprint : arXiv:1011.1418
Keywords : Tracy-Widom law, GUE ensemble, Painlevé II, spectral curve, symplectic invariants, topological recursion, double scaling limit
Numéro Exterieur : CERN-PH-TH/2010-265
Langue : Anglais

Fichier(s) à télécharger :
  • 1011.1418v2

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