A Functional Combinatorial Central Limit Theorem
A Functional Combinatorial Central Limit Theorem
复制标题
泛函组合中心极限定理
DOI：
--
复制
发表时间：
2009
期刊：
影响因子：
--
通讯作者：
S. Janson
中科院分区：
文献类型：
--
作者：
A. Barbour;S. Janson
论文建立了 Hoeffding 组合中心极限定理的函数版本。首先，定义了预限制高斯过程近似，并显示其与原始随机过程的距离为李雅普诺夫比的量级。距离是通过比较过程的平滑泛函的期望来测量的，并且通过斯坦因方法进行论证。然后显示预限制过程在弱条件下收敛到高斯极限过程。该定理用于描述随机排列表的形状。
The paper establishes a functional version of the Hoeffding combinatorial central limit theorem. First, a pre-limiting Gaussian process approximation is defined, and is shown to be at a distance of the order of the Lyapounov ratio from the original random process. Distance is measured by comparison of expectations of smooth functionals of the processes, and the argument is by way of Stein's method. The pre-limiting process is then shown, under weak conditions, to converge to a Gaussian limit process. The theorem is used to describe the shape of random permutation tableaux.