Combinatorics and Computing Weekly Seminar
Limit of Low-Intensity Poisson-Voronoi Tessellation on the Diestel-Leader Graph
Limit of Low-Intensity Poisson-Voronoi Tessellation on the Diestel-Leader Graph
Ali Khezeli, IPM
4 DEC 2024
14:00 - 15:00
The Poisson point process is a random discrete set of points scattered in a metric space X (equipped with a volume measure). The corresponding Voronoi tessellation of X is the well-studied Poisson-Voronoi tessellation. Surprisingly, it has been observed only in the last few years that, if the intensity of the Poisson point process is changed and let converge to zero (and hence, the nuclei of the tessellation escape to infinity), the tessellation itself might not vanish in the limit. This phenomenon has been first observed for regular trees and for hyperbolic spaces. It has also found some important applications; e.g., on the Cheeger constant of hyperbolic surfaces and the cost problem of Lie groups. In this talk, after reviewing the above materials, we will study the limiting tessellation on the Diestel-Leader graph. We will introduce some qualitative properties of the cells and some distributional properties. This is based on ongoing work with Matteo D'Achille.
Zoom room information:
https://us06web.zoom.us/j/85237260136?pwd=MFSZoKdmRXAjfaSaBzbf19lTaaKglf.1
Meeting ID: 852 3726 0136
Passcode: 362880
Venue: Niavaran, Lecture Hall 1