[Todos CMAT] Seminario Sistemas Dinámicos

Matias Carrasco matiascapi en gmail.com
Mie Sep 23 21:05:38 UYT 2015


este viernes 25/9 a las 14:30 en el salón de seminarios del IMERL tenemos el placer de recibir a Elliot Paquette (Weizmann Institut, Israel).

Abajo titulo y resumen.


Title:  The Poisson Voronoi tessellation in hyperbolic space


We consider the hyperbolic Poisson Voronoi (HPV) tessellation,  a
probability measure on tilings of hyperbolic space whose vertices 
are given by a homogeneous Poisson point process.  These tilings are not
quasi-isometric to hyperbolic space, as arbitrarily large tiles and
arbitrarily small tiles may appear.  Nevertheless, we show that
they have "anchored expansion" with probability 1, a relaxation of
non-amenability.  Due to symmetries of hyperbolic space,
the dual graph of HPV is an example of a unimodular random graph.
This, together with anchored expansion, allows us to conclude
many properties of HPV, such as the random walk moving from its
starting point with linear speed.

This is based on joint works with Itai Benjamini, Yoav Krauz, and Josh Pfeffer.
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