Abstract
In this chapter we discuss how Mirzakhani’s curve counting theorem can be used to study statistics of square-tiled surfaces. For example, we compute the probability that, at the same time, both the vertical and horizontal foliations of a closed square-tiled surface of genus 2 and area at most L →∞ are one-cylinder foliations.
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Erlandsson, V., Souto, J. (2022). Counting Square-Tiled Surfaces. In: Mirzakhani’s Curve Counting and Geodesic Currents. Progress in Mathematics, vol 345. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-08705-9_10
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DOI: https://doi.org/10.1007/978-3-031-08705-9_10
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