Publication : t04/019

Semiclassical Orthogonal Polynomials, Matrix Models and Isomonodromic Tau Functions

Bertola M. (Centre de Recherches Mathématiques (CMR), Université de Montréal C.P. 6128, succ. centre ville, Montréal, Québec H3C 3J7, CANADA)
Eynard B. (CEA, DSM, SPhT (Service de Physique Théorique), F-91191 Gif-sur-Yvette, FRANCE)
Harnad J. (Centre de Recherches Mathématiques (CMR), Université de Montréal C.P. 6128, succ. centre ville, Montréal, Québec H3C 3J7, CANADA)
Abstract:
The differential systems satisfied by orthogonal polynomials with arbitrary semiclassical measures supported on contours in the complex plane are derived, as well as the compatible systems of deformation equations obtained from varying such measures. These are shown to preserve the generalized monodromy of the associated rank-$2$ rational covariant derivative operators. The corresponding matrix models, consisting of unitarily diagonalizable matrices with spectra supported on these contours are analyzed, and it is shown that all coefficients of the associated spectral curves are given by logarithmic derivatives of the partition function or, more generally, the gap probablities. The associated isomonodromic tau functions are shown to coincide, within an explicitly computed factor, with these partition functions.
Année de publication : 2006
Revue : Commun. Math. Phys. 263 401-437 (2006)
DOI : 10.1007/s00220-005-1505-4
Preprint : arXiv:nlin.SI/0410043
Numéro Exterieur : CRM-3169_(octobre_2004)
Langue : Anglais

Fichier(s) à télécharger :
  • publi.pdf

  •  

    Retour en haut