Publication : t10/187
The asymptotic expansion of 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:Année de publication : 2010
We establish the relation between two objects: an integrable system related to Painlev\'e II equation, and the symplectic invariants of a certain plane curve S(TW). This curve describes the average eigenvalue density of a random hermitian matrix spectrum near a hard edge (a bound for its maximal eigenvalue). This shows that the s -> -infinity asymptotic expansion of Tracy-Widow law F_{GUE}(s), governing the distribution of the maximal eigenvalue in hermitian random matrices, is given by symplectic invariants.
Preprint : arXiv:1012.2752
Keywords : Tracy-Widom law, GUE ensemble, Painlevé II, spectral curve, symplectic invariants, topological recursion
Numéro Exterieur : CERN-PH-TH/2010-297
Langue : Anglais
