高维Stein方法及其应用
Stein's method in high dimensions with applications
摘要：
令$h$是$R^n$上的三次部分可微函数，令$X=(X_1,\dots,X_n)$是实值随机变量的集合，令$Z=(Z_1,\dots,Z_n)$是多元高斯向量。在这篇文章中，我们开发了Stein的方法，给出了误差界的差异$E h(X) - E h(Z)$的情况下，$X$的坐标不一定是独立的，专注于高维情况下$n\to\infty$。为了表达的依赖结构，我们使用Stein耦合，它允许广泛的应用，如经典的占用，局部依赖，居里-外斯模型等，我们也将应用到谢灵顿-柯克帕特里克模型和最后一次通过渗透薄矩形。
英文摘要：
Let $h$ be a three times partially differentiable function on $R^n$, let $X=(X_1,\dots,X_n)$ be a collection of real-valued random variables and let $Z=(Z_1,\dots,Z_n)$ be a multivariate Gaussian vector. In this article, we develop Stein's method to give error bounds on the difference $E h(X) - E h(Z)$ in cases where the coordinates of $X$ are not necessarily independent, focusing on the high dimensional case $n\to\infty$. In order to express the dependency structure we use Stein couplings, which allows for a broad range of applications, such as classic occupancy, local dependence, Curie-Weiss model etc. We will also give applications to the Sherrington-Kirkpatrick model and last passage percolation on thin rectangles.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
