The largest slice of fractal percolation
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915122444763136 |
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| author | Shmerkin, Pablo Suomala, Ville |
| author_facet | Shmerkin, Pablo Suomala, Ville |
| contents | For each $k\ge 3$, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_15039 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The largest slice of fractal percolation Shmerkin, Pablo Suomala, Ville Probability Classical Analysis and ODEs Primary 60D05, Secondary 28A80, 60J85 For each $k\ge 3$, 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. |
| title | The largest slice of fractal percolation |
| topic | Probability Classical Analysis and ODEs Primary 60D05, Secondary 28A80, 60J85 |
| url | https://arxiv.org/abs/2501.15039 |