Work

Universality in random persistent homology and scale-invariant functionals

Year: 2026

Type: article

Abstract: In this paper, we prove a universality result for the limiting distribution of persistence diagrams arising from geometric filtrations over random point processes. Specifically, we consider the distribution of the ratio of persistence values (death/birth), and show that for fixed dimension, homological degree and filtration type (Čech or Vietoris-Rips), the limiting distribution is independent of the underlying point process distribution, i.e., universal. In proving this result, we present a novel general framework for universality in scale-invariant functionals on point processes. Finally, we also provide a number of new results related to Morse theory in random geometric complexes, which may be of an independent interest.

Source: Communications of the American Mathematical Society

DOI: 10.1090/cams/69

Authors: Omer Bobrowski, Primoz Skraba

Language: English

Topic: Topological and Geometric Data Analysis

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Funders: UK Research and Innovation, Leverhulme Trust, Engineering and Physical Sciences Research Council

Awards: G1677187438, G1737457503, G3055956629, G3340358590, G3845669765, Topological Phase Transitions In Stochastic Geometry, G4250920587, G531213743, G6105391141, Mathematical Foundations of Intelligence: An "Erlangen Programme" for AI, G731302573, G8592757369

OpenAlex ID: W7155045645

FWCI:

Cites: 35

Cited by: 1

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