Smoothness of random self-similar measures on the line and the existence of interior points
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866918022954876928 |
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| author | Bárány, Balázs Rams, Michał |
| author_facet | Bárány, Balázs Rams, Michał |
| contents | In this paper, we study the smoothness of the density function of absolutely continuous measures supported on random self-similar sets on the line. We show that the natural projection of a measure with symbolic local dimension greater than 1 at every point is absolutely continuous with Hölder continuous density almost surely. In particular, if the similarity dimension is greater than 1 then the random self-similar set on the line contains an interior point almost surely. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_06008 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Smoothness of random self-similar measures on the line and the existence of interior points Bárány, Balázs Rams, Michał Dynamical Systems Probability 28A80 60G30 60G57 In this paper, we study the smoothness of the density function of absolutely continuous measures supported on random self-similar sets on the line. We show that the natural projection of a measure with symbolic local dimension greater than 1 at every point is absolutely continuous with Hölder continuous density almost surely. In particular, if the similarity dimension is greater than 1 then the random self-similar set on the line contains an interior point almost surely. |
| title | Smoothness of random self-similar measures on the line and the existence of interior points |
| topic | Dynamical Systems Probability 28A80 60G30 60G57 |
| url | https://arxiv.org/abs/2412.06008 |