Multivariate CLT follows from strong Rayleigh property
Multivariate CLT follows from strong Rayleigh property
复制标题
多元 CLT 源自强瑞利性质
DOI：
--
复制
发表时间：
2016
期刊：
影响因子：
--
通讯作者：
Robin Pemantle
中科院分区：
文献类型：
--
作者：
Subhro Ghosh;T. Liggett;Robin Pemantle
设$（X_1，ldots，X_d）$为非负整数随机变量，$f（z_1，ldots，z_d）$为概率母函数。假设f$是真实的稳定的;等价地，假设这个概率分布的极化是强瑞利的。在特定的例子中，例如通过一个决定性的点过程的不相交集合的占用计数，它是已知的~引用{soshnikov 02}，联合分布必须接近多元高斯分布。我们证明这个结论已经从f$的稳定性中得出。
Let $(X_1 , ldots , X_d)$ be random variables taking nonnegative integer values and let $f(z_1, ldots , z_d)$ be the probability generating function. Suppose that $f$ is real stable; equivalently, suppose that the polarization of this probability distribution is strong Rayleigh. In specific examples, such as occupation counts of disjoint sets by a determinantal point process, it is known~cite{soshnikov02} that the joint distribution must approach a multivariate Gaussian distribution. We show that this conclusion follows already from stability of $f$.