University of Cambridge > Talks.cam > Differential Geometry and Topology Seminar > Sums of excursions along random Teichmuller geodesics and volume asymptotics in the moduli space of quadratic differentials

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

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  • UserVaibhav Gadre, Warwick
  • ClockWednesday 11 February 2015, 16:00-17:00
  • HouseMR13.

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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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