论文标题
固定伪随机的伪数发电机和点设置，且恒星差低
Secure pseudorandom bit generators and point sets with low star-discrepancy
论文作者
论文摘要
星际分配是针对单位立方体中设置点的分布分布的定量度量，该点与准蒙特卡罗算法的集成误差密切相关。如今，这些流行的集成规则也适用于非常高维的整合问题。因此，迫切需要差异较低的合理大小的多维点集。 Heinrich，Novak，Wasilkowski和Wotniakowski的开创性结果表明，存在一个正数$ C $，因此，对于每个尺寸$ d $，在$ [0,1）^d $中都设置了一个$ n $ element点，其中最多$ C \ sqrt/n n} $ c \ sqrt/n} $。这是一个纯粹的存在结果，这种点集的明确结构将是非常可取的。这些证明基于$ n $ element点集的随机样本，对于实际应用而言很难实现。 在本文中，我们建议使用安全的伪andom位生成器来生成点集，并使用订单$ o（\ sqrt {d/n}）$的星级拨号。理论上并通过数值实验来支持该建议。
The star-discrepancy is a quantitative measure for the irregularity of distribution of a point set in the unit cube that is intimately linked to the integration error of quasi-Monte Carlo algorithms. These popular integration rules are nowadays also applied to very high-dimensional integration problems. Hence multi-dimensional point sets of reasonable size with low discrepancy are badly needed. A seminal result from Heinrich, Novak, Wasilkowski and Woźniakowski shows the existence of a positive number $C$ such that for every dimension $d$ there exists an $N$-element point set in $[0,1)^d$ with star-discrepancy of at most $C\sqrt{d/N}$. This is a pure existence result and explicit constructions of such point sets would be very desirable. The proofs are based on random samples of $N$-element point sets which are difficult to realize for practical applications. In this paper we propose to use secure pseudorandom bit generators for the generation of point sets with star-discrepancy of order $O(\sqrt{d/N})$. This proposal is supported theoretically and by means of numerical experiments.
