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

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  • Easton Brawley
  • Mason Doyle
  • Robert Niedzialomski

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.

Suggested Citation

  • Easton Brawley & Mason Doyle & Robert Niedzialomski, 2022. "On the 2‐Wasserstein distance for self‐similar measures on the unit interval," Mathematische Nachrichten, Wiley Blackwell, vol. 295(3), pages 468-486, March.
    • Handle: RePEc:bla:mathna:v:295:y:2022:i:3:p:468-486
    DOI: 10.1002/mana.201900299
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    References listed on IDEAS

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    1. Italo Cipriano & Mark Pollicott, 2018. "Stationary measures associated to analytic iterated function schemes," Mathematische Nachrichten, Wiley Blackwell, vol. 291(7), pages 1049-1054, May.
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