Analysis Seminar

Gravitational Allocation to Uniform Points on the Sphere

Yuval Peres, visiting Kent State University

Friday, April 24th, 2020
3:00 PM - 4:00 PM
Zoom ID: 972-0290-8616

Given uniform points on the surface of a two-dimensional sphere, how can we partition the sphere fairly among them? “Fairly” means that each region has the same area. It turns out that if the given points apply a two-dimensional gravity force to the rest of the sphere, then the basins of attraction for the resulting gradient flow yield such a partition-with exactly equal areas, no matter how the points are distributed. This is related to the work of Nazarov-Sodin-Volberg on Gaussian analytic functions. (See the cover of the AMS Notices at Our main result is that this partition minimizes, up to a bounded factor, the average distance between points in the same cell. I will also present an application to almost optimal matching on the sphere, connecting to a classical result of Ajtai, Komlos, and Tusnady (Combinatorica 1984). Joint work with Nina Holden and Alex Zhai.

Event contact: xchen84 at ur dot rochester dot edu