PC Seminar: Statistically self-similar sets on the line: existence of an interior point
- Date
- 28 August 2025, 10:15–11:30
- Location
- Ångström Laboratory, Å/64119
- Type
- Seminar
- Lecturer
- Balázs Bárány (BME Budapest)
- Organiser
- Matematiska Institutionen
- Contact person
- Sascha Troscheit
Balázs Bárány (BME Budapest) gives this seminar. Welcome to join!
Abstract: In this talk, we study the smoothness of the density function of absolutely continuous measures supported on statistically self-similar sets on the line. We show that the natural projection of a measure with symbolic local dimension greater than one at every point is absolutely continuous with a 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. This is a joint work with Michał Rams.
Participte on site or via Zoom link (meeting ID 65089679653).
This is a seminar in our seminar series on Probability and Combinatorics (PC).