Asymptotic Windings of Horocycles

Uperieure S Ormale N Ecole Stable Windings Stable Windings Stable Windings

We derive the asymptotic laws of winding numbers for planar isotropic stable L evy processes and walks of index 2 (0; 2).

Pleating invariants for punctured torus groups

In this paper we give a complete description of the space QF of quasifuchsian punctured torus groups in terms of what we call pleating invariants. These are natural invariants of the boundary ∂C of the convex core of the associated hyperbolic 3-manifold M and give coordinates for the non-Fuchsian groups QF −F . The pleating invariants of a component of ∂C consist of the projective class of its ...

Density and equidistribution of half-horocycles on a geometrically finite hyperbolic surface

On geometrically finite negatively curved surfaces, we give necessary and sufficient conditions for a one-sided horocycle (hu)s≥0 to be dense in the nonwandering set of the horocyclic flow. We prove that all dense one-sided orbits (hu)s≥0 are equidistributed, extending results of [Bu] and [Scha2] where symmetric horocycles (hu)−R≤s≤R were considered.

Horocycles in hyperbolic 3-manifolds

Wiener Soccer and Its Generalization

The trajectory of the ball in a soccer game is modelled by the Brownian motion on a cylinder, subject to elastic reflections at the boundary points (as proposed in [KPY]). The score is then the number of windings of the trajectory around the cylinder. We consider a generalization of this model to higher genus, prove asymptotic normality of the score and derive the covariance matrix. Further, we...