Lengths of saddle connections on random translation surfaces of large genus
Abstract
We determine the distribution of the number of saddle connections on a random translation surface of large genus. More specifically, for genus g tending to infinity, the number of saddle connections with lengths in a given interval [ag, bg] converges in distribution to a Poisson distributed random variable. Furthermore, the numbers of saddle connections associated to disjoint intervals of lengths are independent.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.