Cusp excursions of random geodesics in Weil-Petersson type metrics

2017/09/19 by Vaibhav Gadre, Gadre, Vaibhav, Carlos Matheus +1
Mathematics · #32G15 #37A25 #37D40 #37D50 #53D25 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Stochastic processes and statistical mechanics

paper · doi:10.48550/arxiv.1709.06355

openalex publication_date 2017/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We analyse cusp excursions of random geodesics for Weil--Petersson type incomplete metrics on orientable surfaces of finite type: in particular, we give bounds for maximal excursions. We also give similar bounds for cusp excursions of random Weil--Petersson geodesics on non-exceptional moduli spaces of Riemann surfaces conditional on the assumption that the Weil--Petersson flow is polynomially mixing. Moreover, we explain how our methods can be adapted to understand almost greasing collisions of typical trajectories in certain slowly mixing billiards.

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