Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

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.
Document type :
Preprints, Working Papers, ...
Complete list of metadatas

Cited literature [18 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01631875
Contributor : Wangru Sun <>
Submitted on : Thursday, November 9, 2017 - 5:28:48 PM
Last modification on : Friday, March 27, 2020 - 4:01:24 AM
Document(s) archivé(s) le : Saturday, February 10, 2018 - 2:16:03 PM

File

DimerModelBeadModelAndStandard...
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01631875, version 1

Citation

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

Share

Metrics

Record views

451

Files downloads

177