Journée-séminaire de combinatoire

(équipe CALIN du LIPN, université Paris-Nord, Villetaneuse)

Le 09 octobre 2015 à 12h45 en B107, Stéphane Dartois nous parlera de : Tenseurs aléatoires (soutenance de thèse)

Résumé : During this defense I present pieces of the work I achieved on random tensor models (tensor models for short). I will define colored triangulations and then review their combinatorics. After this is done I show how one can write integral representation of their generating series. These representations are called tensor models. Using this representation I will describe the combinatorial 1/N expansion for two different kinds of models generating specific classes of colored and non-colored combinatorial maps. I will then concentrate on a specific model, that is the simpler non trivial tensor model and explore some of its properties. In particula r I review the properties of its double scaling limit, then using its Hubbard-Stratanovitch representation, I show how one can use matrix models techniques to recover results obtained using combinatorial techniques. I will finally present several results that point towards integrable structures in the framework of random tensor models.

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