论文标题
高维的累积随机距离 - 计算方式
Accumulated Random Distances in High Dimensions -- Ways of Calculation
论文作者
论文摘要
在本说明中，我们通过Yair审查员（应用的数学和优化，被接受为出版）来完善和改进2019年文章中的一些计算，其中通过量度集中的原则对卓越方法进行了分析。为了完整，这里有一些段落在这里重复。然而，对于在球体上积累“步骤”的情况下，参考完成的距离可以用参考角度代替，这使得更简单。在这里，随机转化的作用的处理也相当“清洁”。对于某些标准偏差，这里获得了精确的不平等现象，而不是仅O-Exptressions。根据后一篇文章，提到了一些进一步的设置，没有直接利益，显示了相似的计算产量的结果。
In this note we refine and improve some of the calculations in our 2019 article with Yair Censor (Applied Mathematics and Optimization, accepted for publication) where an analysis of the superiorization method is made via the principle of concentration of measure. Some paragraphs there are repeated here for the sake of completeness. Yet, for the case of accumulating 'steps' on the sphere, reference to distances as done there is replaced by reference to the angles, which makes simpler expressions. The treatment here of the action of a random transformation is also rather 'cleaner'. For some standard deviations, precise inequalities are here obtained rather then just O-expressions. Some further settings are mentioned, of no direct interest as per the latter article, showing results that similar calculations yield.
