DIMER MODEL, BEAD MODEL AND STANDARD YOUNG TABLEAUX: FINITE CASES AND LIMIT SHAPES - Université Pierre et Marie Curie Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2017

DIMER MODEL, BEAD MODEL AND STANDARD YOUNG TABLEAUX: FINITE CASES AND LIMIT SHAPES

Résumé

The bead model is a random point field on Z × R which can be viewed as a scaling limit of dimer model on a hexagon lattice. We formulate and prove a variational principle similar to that of the dimer model, which states that in the scaling limit, the normalized height function of a uniformly chosen random bead configuration lies in an arbitrarily small neighborhood of a surface h_0 that maximizes some functional which we call as entropy. We also prove that the limit shape h_0 is a scaling limit of the limit shapes of a properly chosen sequence of dimer models. There is a map from bead configurations to standard tableaux of a (skew) Young diagram, and the map is measure preserving if both sides take uniform measures. The variational principle of the bead model yields the existence of the limit shape of a random standard Young tableau.
Fichier principal
Vignette du fichier
DimerModelBeadModelAndStandardYoungTableaux.pdf (3.31 Mo) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01631875 , version 1 (09-11-2017)

Identifiants

  • HAL Id : hal-01631875 , version 1

Citer

Wangru Sun. DIMER MODEL, BEAD MODEL AND STANDARD YOUNG TABLEAUX: FINITE CASES AND LIMIT SHAPES. 2017. ⟨hal-01631875⟩
346 Consultations
109 Téléchargements

Partager

Gmail Facebook X LinkedIn More