A lower bound for the interleaving distance on persistence modules is given in terms of matching distance of rank invariants. This offers an alternative proof of the stability of rank invariants. As a further contribution, also the internal stability of the rank invariant is proved in terms of interleavings.
The Rank Invariant Stability via Interleavings / Landi, Claudia. - 13:(2018), pp. 1-10. [10.1007/978-3-319-89593-2_1]
The Rank Invariant Stability via Interleavings
Landi, Claudia
2018
Abstract
A lower bound for the interleaving distance on persistence modules is given in terms of matching distance of rank invariants. This offers an alternative proof of the stability of rank invariants. As a further contribution, also the internal stability of the rank invariant is proved in terms of interleavings.
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