Vaibhav Gadre

In this talk, we will consider cusp excursions of random geodesics for Weil--Petersson type metrics on orientable surfaces of finite
type. In particular, we will explain how to derive bounds for the size of the "maximal" excursions. Furthermore, assuming polynomial mixing
for the Weil--Petersson flow on non-exceptional moduli spaces, we will give similar bounds in the general setting. Our methods rely on
deriving effective ergodic average for mixing flows. This is joint work with Carlos Matheus.