DIMER MODEL, BEAD MODEL AND STANDARD YOUNG TABLEAUX: FINITE CASES AND LIMIT SHAPES
DIMER MODEL, BEAD MODEL AND STANDARD YOUNG TABLEAUX: FINITE CASES AND LIMIT SHAPES
复制标题
二聚体模型、珠子模型和标准年轻表格：有限情况和极限形状
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
W. Sun
中科院分区：
文献类型：
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作者：
W. Sun
头部模型是Z × R上的随机点场，可以看作是六边形晶格上二聚体模型的标度极限。我们制定并证明了一个类似于二聚体模型的变分原理，该变分原理表明，在缩放极限下，均匀选择的随机头结构的归一化高度函数位于表面h_0的任意小邻域，该邻域最大化了一些我们称之为熵的功能。我们还证明了极限形状h_0是适当选择的二聚体模型序列极限形状的标度极限。有一个地图，从头部配置到标准的（倾斜）杨氏图的表格，如果双方采取统一的措施，该地图是测量保持。头模型的变分原理给出了随机标准杨氏表极限形状的存在性。
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.