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SUMMARY:Partial sums of excursions along random geodesics. - Gadre\, V (Un
 iversity of Warwick)
DTSTART:20140617T103000Z
DTEND:20140617T113000Z
UID:TALK53017@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:In the theory of continued fractions\, Diamond and Vaaler show
 ed the following strong law: for almost every expansion\, the partial sum 
 of first n coefficients minus the largest coefficient divided by n log n t
 ends to a limit. We will explain how this generalizes to non-uniform latti
 ces in SL(2\, R) with cusp excursions in the quotient hyperbolic surface g
 eneralizing 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 fo
 r the moduli space of Riemann surfaces. \n
LOCATION:Seminar Room 2\, Newton Institute Gatehouse
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