Entropy and maximal spacings for random partitions
Entropy and maximal spacings for random partitions
复制标题
随机分区的熵和最大间距
DOI：
10.1007/bf00533604
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发表时间：
1978
期刊：
影响因子：
--
通讯作者：
E. Slud
中科院分区：
文献类型：
--
作者：
E. Slud
摘要从两个角度研究了一些特殊的随机点列诱导的单位区间划分的渐近性质。独立同分布(I.I.D.)的划分熵和最大间隔首先将[0，1]中的均匀序列与S.Kakutani方案生成的随机序列的相应量进行比较。然后引入了利用区间分裂树结构的一般组合技术来证明几乎必然(A.S.)Kakutani构造点的均匀分布，以及经验测度收敛到勒贝格测度的速度以及A.S.等其他结果。K-字节组在[0，1]k中的均匀分布
SummaryAsymptotic properties of the partitions of the unit interval induced by some special random sequences of points are studied from two points of view. The partition-entropy and largest spacings for independent identically distributed (i.i.d.) uniform sequences in [0,1] are first compared with the corresponding quantities for a random sequence generated by a scheme of S. Kakutani. A general combinatorial technique exploiting the tree structure of interval splittings is then introduced to prove almost-sure (a.s.) equidistribution of the points of Kakutani's construction, along with a rate of convergence of empirical measures to Lebesgue measure and such other results as a.s. equidistribution of k-tuples in [0,1]k