The largest slice of fractal percolation
Shmerkin, Pablo; Suomala, Ville (2025-11-05)
Avaa tiedosto
Sisältö avataan julkiseksi: 05.11.2026
Springer
05.11.2025
Shmerkin, P., & Suomala, V. (2025). The largest slice of fractal percolation. Research in the Mathematical Sciences, 12(4), 88. https://doi.org/10.1007/s40687-025-00572-0
https://rightsstatements.org/vocab/InC/1.0/
©The Author(s), under exclusive licence to Springer Nature Switzerland AG 2025. This is a post-peer-review, pre-copyedit version of an article published in Research in the Mathematical Sciences. The final authenticated version is available online at: https://doi.org/10.1007/s40687-025-00572-0
https://rightsstatements.org/vocab/InC/1.0/
©The Author(s), under exclusive licence to Springer Nature Switzerland AG 2025. This is a post-peer-review, pre-copyedit version of an article published in Research in the Mathematical Sciences. The final authenticated version is available online at: https://doi.org/10.1007/s40687-025-00572-0
https://rightsstatements.org/vocab/InC/1.0/
Julkaisun pysyvä osoite on
https://urn.fi/URN:NBN:fi:oulu-202604282857
https://urn.fi/URN:NBN:fi:oulu-202604282857
Tiivistelmä
Abstract
For each k≥3, we determine the dimensional threshold for planar fractal percolation to contain k collinear points. In the critical case of dimension 1, the largest linear slice of fractal percolation is a Cantor set of zero Hausdorff dimension. We investigate its size in terms of generalized Hausdorff measures.
For each k≥3, we determine the dimensional threshold for planar fractal percolation to contain k collinear points. In the critical case of dimension 1, the largest linear slice of fractal percolation is a Cantor set of zero Hausdorff dimension. We investigate its size in terms of generalized Hausdorff measures.
Kokoelmat
- Avoin saatavuus [42834]