Poisson approximation of the length spectrum of random surfaces
  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. 
Bram Petri, Christoph Thaele
math.PR math.DG math.GT