The Moments and Distributions of Some Quantities Arising from Random Arcs on the Circle

摘要

This work concerns random arcs on the circle. Arcs with randomly chosen lengths are placed uniformly on the circumference of a circle and probabilistic questions are asked about the resulting configuration. Emphasis is placed on deriving expressions for the moments and joint moments of quantities such as the number of uncovered gaps, the measure of the uncovered region and the length of the largest gap. Distributions are also obtained for some of these variables.