26 04 im alumniV8
22 11 im fatiado face
22 11 im fatiado twitter
22 11 im fatiado youtube
22 11 im fatiado gmail
22 11 im fatiado brazil
22 11 im fatiado england
22 11 im fatiado spain

Probability Webinar 1Título: Gravitational allocation of uniform points on the sphere

Palestrante: Yuval Peres (Kent State University)
Data: 12/04/2021
Horário: 15:00h
Local: Transmissão online

Confira AQUI o link para a transmissão.

Resumo: 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 work of Nazarov-Sodin-Volberg on Gaussian analytic functions. (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 on the sphere, connecting to a classical result of Ajtai, Komlos and Tusnady (Combinatorica 1984).

Joint work with Nina Holden and Alex Zhai.