Sums of excursions along random Teichmuller geodesics and volume asymptotics in the moduli space of quadratic differentials

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• Vaibhav Gadre, Warwick
• Wednesday 11 February 2015, 16:00-17:00
• MR13.

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For a non-uniform lattice in SL(2,R) we prove a strong law for a certain partial sum expressed in terms of excursions of a random geodesic in cusp neighborhoods of the quotient hyperbolic surface/orbifold. This generalizes the theorem by Diamond and Vaaler that for a Lebesgue typical number in (0,1) the sum of the first n continued fraction coefficients minus the largest coefficient is asymptotic to n log n/ log 2. We also show that a similar strong law holds along SL(2,R) orbit closures (shown to be affine invariant submanifolds by Eskin-Mirzakhani and Eskin-Mirzakhani-Mohammadi) in the moduli space of quadratic differentials.

This talk is part of the Differential Geometry and Topology Seminar series.

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