论文标题
聚合物复制品的几何隆起对应关系和分区函数
The geometric Burge correspondence and the partition function of polymer replicas
论文作者
论文摘要
我们构建了Burge对应关系的几何升起，作为通用年轻图形形状阵列上局部Birational图的组成。我们建立了它与几何鲁滨逊 - 史密斯（Robinson-Schensted-Knuth）的基本关系以及与几何Schützenberger的相关性。我们还显示了几何布尔格对应的许多属性，将其专门针对对称输入阵列的情况。特别是，我们的构造表明，这种映射是在日志变量中保存的卷。作为应用程序，我们考虑了一个给定长度的两个聚合物路径的模型，该模型的长度约束为具有相同的端点，称为聚合物副本。我们证明，在log-gamma随机环境中，聚合物复制品分区函数的分布是惠特克度量，并推断出相应的惠特克整体身份。对于某个参数的选择，我们注意到我们的模型与O'Connell，Seppäläinen和Zygouras（2014）研究的模型与对称log-gamma聚合物之间的分布身份。
We construct a geometric lifting of the Burge correspondence as a composition of local birational maps on generic Young-diagram-shaped arrays. We establish its fundamental relation to the geometric Robinson-Schensted-Knuth correspondence and to the geometric Schützenberger involution. We also show a number of properties of the geometric Burge correspondence, specializing them to the case of symmetric input arrays. In particular, our construction shows that such a mapping is volume preserving in log-log variables. As an application, we consider a model of two polymer paths of given length constrained to have the same endpoint, known as polymer replica. We prove that the distribution of the polymer replica partition function in a log-gamma random environment is a Whittaker measure, and deduce the corresponding Whittaker integral identity. For a certain choice of the parameters, we notice a distributional identity between our model and the symmetric log-gamma polymer studied by O'Connell, Seppäläinen, and Zygouras (2014).
