Campuses:

Statistical Regularities of Self-Intersection Counts for Geodesics on Negatively Curved Surfaces

Wednesday, October 30, 2013 - 10:15am - 11:05am
Keller 3-180
Steven Lalley (University of Chicago)
Let U be a compact, negatively curved surface. From the
(finite) set of all closed geodesics on U of length less than L
choose one, and let N (L) be the number of its self-intersections.
There is a positive constant $K$ such that with overwhelming
probability as L grows,

N (L)/L^{2} approaches K.

This talk will concern itself with fluctuations. The main theorem
states that if U has variable negative curvature then

(N (L)-KL^{2})/L^{3/2}

converges in distribution to a Gaussian law,
but if U has constant negative curvature then

(N (L)-KL^{2})/L

converges in distribution to a (probably) non-Gaussian law.
MSC Code: 
53C22
Keywords: