论文标题
多政治随机分区
Multicritical random partitions
论文作者
论文摘要
我们研究了两个对整数分区的概率措施的家族，它们是Schur度量的，其参数以与通用$ 1/3 $不同的关键指数为特征的参数。我们发现，第一部分渐近地遵循Tracy-Widom Gue分布的“高阶类似物”，该分布以前在量子统计物理学中遇到了Le Doussal，Majumdar和Schehr。我们还计算限制形状，并讨论我们一个家庭和Periwal和Shevitz引入的多政治统一矩阵模型之间的精确映射。
We study two families of probability measures on integer partitions, which are Schur measures with parameters tuned in such a way that the edge fluctuations are characterized by a critical exponent different from the generic $1/3$. We find that the first part asymptotically follows a "higher-order analogue" of the Tracy-Widom GUE distribution, previously encountered by Le Doussal, Majumdar and Schehr in quantum statistical physics. We also compute limit shapes, and discuss an exact mapping between one of our families and the multicritical unitary matrix models introduced by Periwal and Shevitz.
