New Results for the Stability of Persistence Diagrams

Stability is certainly one most important aspect of persistence and there are numerous results. Most of the results are in terms of bottleneck distance between persistence diagrams. While applicable in general settings, it is a sup-norm, and using it to prove convergence can be difficult. In this talk, I will discuss some new results concentrating on a bound on the p-Wasserstein distance between persistence diagrams. The main result states that p-norm between two functions on a simplicial complex is an upper bound on the p-Wasserstein distance between the corresponding persistence diagrams. I will discuss some other related results as well as applications.