60 years of dynamics and number expansions

From continued fractions to random walks on hyperbolic manifolds

speaker: Giulio Tiozzo (Yale University)

abstract: A well-known and amusing fact which goes back to Khinchin states that for almost every point in the unit interval, the arithmetic mean of its continued fraction coefficients goes to infinity, while the geometric mean converges to a constant.

We will see how this fact can be interpreted geometrically in terms of the distribution of the excursion of random geodesics in the cusp of a hyperbolic surface. This will then be used to show that the Lebesgue measure on the boundary of hyperbolic n-space is not in the same class as the hitting measure for a random walk.

Based on joint work with V. Gadre and J. Maher, and more recently with A. Randecker.

timetable:
Thu 13 Dec, 15:00 - 15:45, Aula Dini
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