Accumulated Random Distances in High Dimensions -- Ways of Calculation
Abstract
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.
Cite
@article{arxiv.2003.10941,
title = {Accumulated Random Distances in High Dimensions -- Ways of Calculation},
author = {Eliahu Levy},
journal= {arXiv preprint arXiv:2003.10941},
year = {2020}
}
Comments
20 pages. This is a sort of companion/supplement to our arXiv:1909.00398 with Yair Censor