I am looking for references to problems related to computing the statistical properties of uniformly randomly chosen points or arcs on the unit circle, e.g.:
On a unit circle, $n$ points are chosen uniformly randomly. What is the expected angular distance between nearest neighbours on the circle? What is the variance of the (angular) distance between farthest points?
On a unit circle, $n$ disjoint arcs of the same length $l$ are selected at random. What is the expected (angular) distance between the nearest endpoints of consecutive arcs?
One promising example seems to be Order Statistics by David and Nagaraja, but Google books won't let me see much of this book. I am able to find scattered references that address specific sub-problems, e.g. this 1939 paper by Wesley that addresses overlapping arcs on the circle. But I'd appreciate an exhaustive reference if there's one.