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Fredholm determinants and non-commutative Painlevé equations.

Le : 08/10/2013 14h00
Par : Mattia Cafasso (LAREMA)
Lieu : I 103
Lien web :
Résumé : It has been known since the nineties that some important quantities arising in random matrix theory (gap probabilities) can be expressed either as Fredholm determinants of integrable operators or as "special" solutions of Painlevé equations (e.g. the celebrated Tracy--Widom distribution). After a brief account of some of the main results in this field, I will discuss the generalization to the non-commutative setting. More specifically, I will give some examples of solutions to non--commutative Painlevé equations that can be equivalently expressed as Fredholm determinants. All the results mentioned in this talk have been obtained in joint works with Marco Bertola and Manuel Dominguez de la Iglesia.