Gaussian processes can be considered as subsets of a standard Hilbert space, but the geometric understanding that would relate the size of a set with the size of its convex hull is still lacking. In this work, we adopt a geometric approach to the majorizing measure problem by identifying the covering number relationships between a given space $T$ and its convex hull, represented by $T_h$. If the space $T$ is a closed bounded polyhedra in $\mathbb{R}^n$, we can evaluate the volume ratio between the space $T$ and its convex hull obtained by the Quickhull algorithm. If the space $T$ is a general compact object in $\mathbb{R}^n$ with non-empty interior, we first establish a more general reverse Brunn-Minkowski inequality for nonconvex spaces which will assist us to bound the volume of $T_h$ in terms of the volume of $T$ if $T_h$ can be acquired by the finite average of the space $T$ with respect to the Minkowski sum. If the volume ratio between the space $T$ and the space $T_h$ is obtained, the covering number ratio between the space $T$ and the space $T_h$ can also be obtained which will be used to build majorizing measure inequality. For infinite dimensional space, we show that the constant $L$ at majorizing measure inequality may not always exist and the existence condition will depend on geometric properties of $T$.
Joint large deviation result for empirical measures of the coloured random geometric graphs
证明了\emph{near intermediate}有色随机几何图模型的\emph{ empirical pair measure}和\emph{empirical locality measure}在单位圆周$d-$维环面上均匀选取的$n$点上的联合大偏差原理，由此得到了\emph{number of edges per vertex}的大偏差原理，\emph{near intermediate}随机几何图模型的\emph{degree distribution and the proportion of isolated vertices }.
Generalized Arithmetic and Geometric Mean Divergence Measure and their Statistical Aspects
利用Blackwell关于比较两个实验的定义，对具有一个和两个标量参数的\textit{generalized AG - divergence}测度进行了比较。给出了\textit{generalized AG - divergence}测度与\textit{Fisher measure of information}的联系。本文还提出了统一的\textit{generalization of AG - divergence}和\textit{Jensen-Shannon divergence measures}。
