February 7, 10:30.

Speaker: Vincent Divol (INRIA).

Title : On representations of persitence diagrams in a random setting

I will present some of the works I did during my first year in the Datashape team, focusing on theoretical results on the representations of persistence diagrams (e.g. persistence images, persistence silhouettes, etc.) in a random setting. More specifically, we show that: 1) under suitable conditions, the expected persistence diagram, which is a measure supported on the upper half plane, has a (smooth) density with respect to the Lebesgue measure. 2) when building the persistence diagram for the Rips or Cech filtration on a sample made of n points, there exists a limit persistence diagram when n goes to infinity. We are able to study some properties of this limit object. Those two results give hindsight on the behaviors of representations of persistence diagrams.