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

Abstract : 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.
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Pré-publication, Document de travail
2017
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https://hal.archives-ouvertes.fr/hal-01631875
Contributeur : Wangru Sun <>
Soumis le : jeudi 9 novembre 2017 - 17:28:48
Dernière modification le : samedi 11 novembre 2017 - 01:11:41

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  • HAL Id : hal-01631875, version 1

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INSMI | UPMC | USPC | PMA

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Wangru Sun. DIMER MODEL, BEAD MODEL AND STANDARD YOUNG TABLEAUX: FINITE CASES AND LIMIT SHAPES. 2017. 〈hal-01631875〉

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