Gravitational allocation to uniform points on the sphere

Gravitational allocation to uniform points on the sphere

Probability Seminar
May 9, 2018, 03:10 PM - 04:00 PM | 1011 Evans Hall | Happening As Scheduled
Yuval Peres, Microsoft Research
Given n 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...