Given a basepoint in Teichmuller space, a measure on the
Thurston boundary can be used
to sample at random a geodesic ray from the basepoint. In particular,
we consider two families of
measures: the ones which belong to the Lebesgue or visual measure
class, and harmonic
measures for random walks on the mapping class group generated by a
finitely supported distribution.
Along a geodesic ray, we consider the ratio between the word metric
and the relative metric of
approximating mapping class group element. We prove that this ratio
tends to infinity along a
Lebesgue-typical geodesic ray, and is finite along geodesics along a
harmonic-typical geodesic ray.
As a corollary, we give a different proof of singularity of harmonic
measure. The same proof works for
Fuchsian groups with cusps. This is joint work with Joseph Maher
(CUNY) and Giulio Tiozzo (Harvard).
Word length statistics along random Teichmuller geodesics
Event time:
Monday, March 4, 2013 - 11:30am to 12:30pm
Location:
431 DL
Speaker:
Vaibhav Gadre
Speaker affiliation:
Harvard
Event description: