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Hydrodynamic limit for a dynamic model of 2D Young diagrams

le 28 avril 2010

14H - Groupe de travail "Applications des Mathématiques"

ENS Rennes Bâtiment Sauvy, Salle 5 (rdc)
Plan d'accès

Séminaire de Tadahisa Funaki (Université de Tokyo) au groupe de travail "Applications des mathématiques"

Lien vers la page Web de l'orateur Résumé : We consider dynamics of two-dimensional Young diagrams by allowing the creation and annihilation of unit squares located at the boundary of the diagrams.  The dynamics are naturally associated with the grandcanonical ensembles introduced by Vershik ('96), which are uniform measures under conditioning on their area.  We show that, as the averaged area of the diagrams diverges, the corresponding height variable converges to a solution of a certain non-linear partial differential equation under a hydrodynamic space-time scaling. The stationary solution of the limit equation is identified with the so-called Vershik curve.  We also discuss the conservative dynamics which have a connection to the surface diffusion, and give some remarks to the 3D case.  This is a joint work with Makiko Sasada (Univ Tokyo) and the paper will appear in Comm. Math. Phys.

Recherche - Valorisation
Virginie Bonnaillie-Noël, Yannick Privat et Grégory Vial

Mise à jour le 6 avril 2010