论文标题
限制简单中随机点的定理
Limit theorems for random points in a simplex
论文作者
论文摘要
在这项工作中，研究了$ \ ell_q $ -norms在高维的集中常规单纯形中随机选择的点的点。在制度中的贝里 - 埃斯尼（Berry-Esseen）界限$ 1 \ leq q <\ infty $是由非中央限制定理得出和补充的，在$ q = \ infty $的情况下，中等和大偏差。还进行了与$ \ ell_p^n $ -balls的相应结果的比较。
In this work the $\ell_q$-norms of points chosen uniformly at random in a centered regular simplex in high dimensions are studied. Berry-Esseen bounds in the regime $1\leq q < \infty$ are derived and complemented by a non-central limit theorem together with moderate and large deviations in the case where $q=\infty$. A comparison with corresponding results for $\ell_p^n$-balls is carried out as well.
