论文标题
广义的福拉巴尔不平等，改进的括号封面以及申请差异
A Generalized Faulhaber Inequality, Improved Bracketing Covers, and Applications to Discrepancy
论文作者
论文摘要
我们证明了普遍的Faulhaber不平等，以限制第一个$ n $（可能移动）自然数的$ j $ th权力的总和。在这种不平等的帮助下，我们能够改善已知的界限，以固定在$ 0 $的$ d $二维轴平行盒中（或者以不同的方式放置）与$ d $ d $ d $ d $二维单元cube $ [0,1]^d $相交的左下矫形器。我们使用这些改进的括号数字来为负相关的随机点集及其期望的星级验证建立新的界限。我们还将发现也应用于加权的星际票据。
We prove a generalized Faulhaber inequality to bound the sums of the $j$-th powers of the first $n$ (possibly shifted) natural numbers. With the help of this inequality we are able to improve the known bounds for bracketing numbers of $d$-dimensional axis-parallel boxes anchored in $0$ (or, put differently, of lower left orthants intersected with the $d$-dimensional unit cube $[0,1]^d$). We use these improved bracketing numbers to establish new bounds for the star-discrepancy of negatively dependent random point sets and its expectation. We apply our findings also to the weighted star-discrepancy.
