Euler and Betti curves are stable under Wasserstein deformations of distributions of stochastic processes - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Preprints, Working Papers, ... (Preprint) Year : 2022

Euler and Betti curves are stable under Wasserstein deformations of distributions of stochastic processes

Abstract

Euler and Betti curves of stochastic processes defined on a $d$-dimensional compact Riemannian manifold which are almost surely in a Sobolev space $W^{n,s}(X, \mathbb{R})$ (with $d < n$) are stable under perturbations of the distributions of said processes in a Wasserstein metric. Moreover, Wasserstein stability is shown to hold for all $p > \frac{d}{n}$ for persistence diagrams stemming from functions in $W^{n,s}(X, \mathbb{R})$.
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Dates and versions

hal-03906966 , version 1 (19-12-2022)

Identifiers

  • HAL Id : hal-03906966 , version 1

Cite

Daniel Perez. Euler and Betti curves are stable under Wasserstein deformations of distributions of stochastic processes. 2022. ⟨hal-03906966⟩
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