Font Size:

Pólya's method to construct Voronoi diagrams

Building: Mykhailo Drahomanov National Pedagogical University

Room: Room A

Date: 2018-09-25 11:15 AM – 12:00

Last modified: 2018-09-23

#### Abstract

Pólya's Shire theorem from 1927 says that the zero sets $Z(f^{(n)})$ of the iterated derivatives $f^{(n)}$ of a meromorphic function $f$ with set of poles $S$ accumulate along (the boundaries of) the Voronoi diagram associated with $S$. But it leaves open the question of the asymptotic distribution of the zero-set. We will show that the answer is interesting, leading to a probability measure on Voronoi diagrams, by describing what is known for some classes of functions, and also discuss possible extensions to higher dimensions.