高维正态分布族Fisher度量的曲率
Curvature Properties of Fisher Metrics for High-Dimensional Normal Distribution Families

本文针对高维情形得到了高维正态分布在Fisher度量下的数量曲率，并且证明了当协方差矩阵Σ为对角矩阵时，正态分布族的参数空间是爱因斯坦空间，其Ricci曲率与度量张量成严格比例关系。
In this paper, the scalar curvature of high-dimensional normal distribution under Fisher metric is obtained for the high-dimensional case, and it is proved that when the covariance matrix Σ is a diagonal matrix, the parameter space of the normal distribution family is Einstein space, and its Ricci curvature is strictly proportional to the metric tensor.