Smoothness of random self-similar measures on the line and the existence of interior points
Abstract 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.
Authors
- Balázs Bárány (ORCID: https://orcid.org/0000-0002-0129-8385)
- Michał Rams (ORCID: https://orcid.org/0000-0001-9816-5492)
Institutions
- HUN-REN Alfréd Rényi Institute of Mathematics (HU)
- Budapest University of Technology and Economics (HU)
- Institute of Mathematics (PL)
- Polish Academy of Sciences (PL)
Publication Details
- Journal
- Probability Theory and Related Fields
- Published
- 2025-06-11
- DOI
- https://doi.org/10.1007/s00440-025-01389-2
- Primary Topic
- Mathematical Dynamics and Fractals
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Budapesti Műszaki és Gazdaságtudományi Egyetem
- Narodowym Centrum Nauki
- Nemzeti Kutatási Fejlesztési és Innovációs Hivatal
- Nemzeti Kutatási, Fejlesztési és Innovaciós Alap