Poisson approximation of the length spectrum of random surfaces

Abstract

Multivariate Poisson approximation of the length spectrum of random surfaces is studied by means of the Chen-Stein method. This approach delivers simple and explicit error bounds in Poisson limit theorems. They are used to prove that Poisson approximation applies to curves of length up to order $o(\log \log g)$ with $g$ being the genus of the surface.

arXiv comment22 pages, 2 figures. To appear in Indiana Univ. Math. J