In this talk I will talk about some new results for the escape and
hitting statistics for various open dynamical systems. This includes
1. Poisson limit laws for arbitrary slow mixing hyperbolic billiards,
a connection to RH will be presented too
2. polynomial and exponential escape rates, and
3. where orbits prefer going in the phase space of nonuniformly
expanding dynamical systems. I will outline the idea of the proof for
it, which uses operator renewal theory and generalized Keller-Liverani
perturbation theory.

This is a joint work with Prof. Bunimovich.