Cusp excursions of random geodesics in Weil-Petersson type metrics

Gadre, V. and Matheus, C. (2020) Cusp excursions of random geodesics in Weil-Petersson type metrics. Journal of Differential Geometry, (Accepted for Publication)

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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.

Item Type:Articles
Status:Accepted for Publication
Refereed:Yes
Glasgow Author(s) Enlighten ID:Gadre, Dr Vaibhav
Authors: Gadre, V., and Matheus, C.
Subjects:Q Science > QA Mathematics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Journal of Differential Geometry
Publisher:International Press
ISSN:0022-040X
ISSN (Online):1945-743X
Copyright Holders:Copyright © 2020 The Authors
First Published:First published in Journal of Differential Geometry 2020
Publisher Policy:Reproduced in accordance with the publisher copyright policy
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