Aarhus University Seal

Extremal lifetimes of persistent cycles

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review

Persistent homology captures the appearances and disappearances of topological features such as loops and cavities when growing disks centered at a Poisson point process. We study extreme values for the lifetimes of features dying in bounded components and with birth resp. death time bounded away from the threshold for continuum percolation and the coexistence region. First, we describe the scaling of the minimal lifetimes for general feature dimensions, and of the maximal lifetimes for cavities in the Cech filtration. Then, we proceed to a more refined analysis and establish Poisson approximation for large lifetimes of cavities and for small lifetimes of loops. Finally, we also study the scaling of minimal lifetimes in the Vietoris-Rips setting and point to a surprising difference to the Cech filtration.

Original languageEnglish
Pages (from-to)299-330
Number of pages32
Publication statusPublished - Jun 2022

    Research areas

  • Topological data analysis, Persistent Betti numbers, Poisson approximation, TOPOLOGY, LIMIT, 82C22, 60K35

See relations at Aarhus University Citationformats

ID: 228048449