On the 2‐Wasserstein distance for self‐similar measures on the unit interval

Easton Brawley, Mason Doyle and Robert Niedzialomski

Mathematische Nachrichten, 2022, vol. 295, issue 3, 468-486

Abstract: We obtain a lower and an upper bound for the 2‐Wasserstein distance between self‐similar measures associated to two increasing non‐overlapping linear contractions of the unit interval. We use a method of approximation of the measures via iterations of the Hutchinson operator on a delta Dirac measure. This allows us to obtain explicit estimates for the 2‐Wasserstein distance between the approximating measures. We use these bounds to obtain the bounds for the distance between the self‐similar measures.

Date: 2022
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https://doi.org/10.1002/mana.201900299

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