Central limit theorems for counting measures in coarse negative curvature
Giulio Tiozzo (University of Toronto (Canada))
Abstract: We establish general central limit theorems for an action of a group on a hyperbolic space with respect to counting for the word length in the group. In 2013, Chas, Li, and Maskit produced numerical experiments on random closed geodesics on a hyperbolic pair of pants. Namely, they drew uniformly at random conjugacy classes of a given word length, and considered the hyperbolic length of the corresponding closed geodesic on the pair of pants. Their experiments lead to the conjecture that the length of these closed geodesics satisfies a central limit theorem, and we proved this conjecture in 2018. In our new work, we remove the assumptions of properness and smoothness of the space, or cocompactness of the action, thus proving a general central limit theorem for group actions on hyperbolic spaces. We will see how our techniques replace the classical thermodynamic formalism and allow us to provide new applications, including to lengths of geodesics in geometrically finite manifolds and to intersection numbers with submanifolds. Joint work with I. Gekhtman and S. Taylor.
dynamical systems
Audience: researchers in the topic
Comments: Zoom link: unipd.zoom.us/j/91001776009?pwd=Qm0wZVF3TWxmNm9LVFhYL0RiczBHdz09
DinAmicI: Another Internet Seminar
Series comments: For more information and for the instructions to obtain the link to the seminars, visit:
Moreover, most seminars will be streamed live on the DinAmicI YouTube channel:
www.youtube.com/channel/UCyNNg155G3iLS7l-qZjboyg
Organizers: | Alessandra Bianchi, Claudio Bonanno, Marco Lenci, Marcello Seri, Alfonso Sorrentino* |
*contact for this listing |