Dimer model, bead model and standard Young tableaux: finite cases and limit shapes
| Autor: | Sun, Wangru |
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| Rok vydání: | 2018 |
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| Druh dokumentu: | Working Paper |
| Popis: | The bead model is a random point field on $\mathbb{Z}\times\mathbb{R}$ which can be viewed as a scaling limit of dimer model. We prove 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 preserves uniform measures, and our results of the bead model yield the existence of the limit shape of a random standard Young tableau. Comment: 67 pages, 15 figures |
| Databáze: | arXiv |
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