论文标题
不均匀U统计量的自民党
LDP for Inhomogeneous U-Statistics
论文作者
论文摘要
在本文中，我们得出了一个较大的偏差原理（LDP），以实现通用顺序不均匀的U/V统计量。使用此情况，我们为两种类型的统计数据得出了一份LDP：随机多线性形式和子图的单色副本数量。我们表明，在这些情况下，相应的速率函数可以表示为在合适的功能空间上的变异问题。我们使用开发的工具来研究与相应的哈密顿人的吉布斯度量，其中包括对Ising（具有非紧密基础措施）和Potts模型的张量概括。对于这些Gibbs的措施，我们建立了对数正常化常数的缩放限制，并且根据弱*拓扑而弱的法律，这可能是独立的利益。
In this paper we derive a Large Deviation Principle (LDP) for inhomogeneous U/V-statistics of a general order. Using this, we derive a LDP for two types of statistics: random multilinear forms, and number of monochromatic copies of a subgraph. We show that the corresponding rate functions in these cases can be expressed as a variational problem over a suitable space of functions. We use the tools developed to study Gibbs measures with the corresponding Hamiltonians, which include tensor generalizations of both Ising (with non-compact base measure) and Potts models. For these Gibbs measures, we establish scaling limits of log normalizing constants, and weak laws in terms of weak* topology, which are of possible independent interest.
