Partial sums of excursions along random geodesics.
Duration: 59 mins 47 secs
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About this item
| Description: |
Gadre, V (University of Warwick)
Tuesday 17 June 2014, 11:30-12:30 |
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| Created: | 2014-07-09 15:26 |
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| Collection: | Interactions between Dynamics of Group Actions and Number Theory |
| Publisher: | Isaac Newton Institute |
| Copyright: | Gadre, V |
| Language: | eng (English) |
| Distribution: |
World
(downloadable)
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| Explicit content: | No |
| Aspect Ratio: | 16:9 |
| Screencast: | No |
| Bumper: | UCS Default |
| Trailer: | UCS Default |
| Abstract: | In the theory of continued fractions, Diamond and Vaaler showed the following strong law: for almost every expansion, the partial sum of first n coefficients minus the largest coefficient divided by n \log n tends to a limit. We will explain how this generalizes to non-uniform lattices in SL(2, R) with cusp excursions in the quotient hyperbolic surface generalizing continued fraction coefficients. The general theorem relies on the exponential mixing of geodesic flow, in particular on the fast decay of correlations due to Ratner. Analogously, similar theorems are true for the moduli space of Riemann surfaces. |
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