Work

Smoothness of random self-similar measures on the line and the existence of interior points

Year: 2025

Type: article

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.

Source: Probability Theory and Related Fields

DOI: 10.1007/s00440-025-01389-2

Authors: Balázs Bárány, Michał Rams

Institutions: Budapest University of Technology and Economics, HUN-REN Alfréd Rényi Institute of Mathematics, Institute of Mathematics, Polish Academy of Sciences

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funders: Budapesti Műszaki és Gazdaságtudományi Egyetem, Narodowym Centrum Nauki, Nemzeti Kutatási Fejlesztési és Innovációs Hivatal, Nemzeti Kutatási, Fejlesztési és Innovaciós Alap