Distribution of intersection lengths of a random geodesic with a   geodesic lamination
  We investigate the distribution of lengths obtained by intersecting a random geodesic with a geodesic lamination. We give an explicit formula for the distribution for the case of a maximal lamination and show that the distribution is independent of the surface and lamination. We also show how the moments of the distribution are related to the Riemann zeta function. 
Martin Bridgeman and David Dumas