论文标题
晶格类型的间隔类型本地限制定理随机变量和分布
Interval Type Local Limit Theorems for Lattice Type Random Variables and Distributions
论文作者
论文摘要
在本文中，我们提出了对晶格单变量和多变量分布的局部极限定理的新解释。我们表明 - 从标准意义上讲，给定局部极限定理 - 分布通过极限分布很好地近似，在可能衰减长度的间隔上均匀地分布。我们确定间隔长度的最大允许衰减速度。此外，我们表明，对于连续分布，间隔类型的本地法律在间隔长度上没有任何衰减速度限制。我们显示，该框架中的各种示例，例如I.I.D.的标准化总和。由统计力学的多维自旋模型诱导的随机向量或相关的随机矢量。
In this paper, we propose a new interpretation of local limit theorems for univariate and multivariate distributions on lattices. We show that - given a local limit theorem in the standard sense - the distributions are approximated well by the limit distribution, uniformly on intervals of possibly decaying length. We identify the maximally allowable decay speed of the interval lengths. Further, we show that for continuous distributions, the interval type local law holds without any decay speed restrictions on the interval lengths. We show that various examples fit within this framework, such as standardized sums of i.i.d. random vectors or correlated random vectors induced by multidimensional spin models from statistical mechanics.
