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