Comment Feed for Channel 9 - Pacific Northwest Probability Seminar: Gravitational Allocation to Uniform Points on the Spherehttp://video.ch9.ms/ch9/4762/0bb52488-06f7-4077-a2f2-00faca5e4762/39978_220.jpgChannel 9 - Pacific Northwest Probability Seminar: Gravitational Allocation to Uniform Points on the SphereGiven 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 the points are distributed. (See the cover of the AMS Notices at http://www.ams.org/publications/journals/notices/201705/rnoti-cvr1.pdf.) 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 of n uniform blue points to n uniform red points on the sphere, connecting to a classical result of Ajtai, Komlos and Tusnady (Combinatorica 1984). Joint work with Nina Holden and Alex Zhai. enSat, 11 Jul 2020 11:25:56 GMTSat, 11 Jul 2020 11:25:56 GMTRev9