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Wasserstein distance for generalized persistence modules and abelian categories Scott, Jonathan

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In persistence theory and practice, measuring distances between modules is central. The Wasserstein distances are the standard family of $L^p$ distances (with $1 \leq p \leq \infty$) for persistence modules. We give an algebraic formulation of these distances. For $p=1$ it generalizes to abelian categories and for arbitrary $p$ it generalizes to Krull-Schmidt categories. These distances may be useful for the computation of distance between generalized persistence modules. This is joint work with Peter Bubenik and Donald Stanley.

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Attribution-NonCommercial-NoDerivatives 4.0 International