Minkowski sum of fractal percolation and random sets
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912632830689280 |
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| author | Bai, Tianyi Chen, Xinxin Peres, Yuval |
| author_facet | Bai, Tianyi Chen, Xinxin Peres, Yuval |
| contents | In this paper, we prove that hitting probability of Minkowski sum of fractal percolations can be characterized by capacity. Then we extend this result to Minkowski sum of general random sets in $\mathbb Z^d$, including ranges of random walks and critical branching random walks, whose hitting probabilities are described by Newtonian capacity individually. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_16415 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Minkowski sum of fractal percolation and random sets Bai, Tianyi Chen, Xinxin Peres, Yuval Probability 60G22, 60J05, 60K35 In this paper, we prove that hitting probability of Minkowski sum of fractal percolations can be characterized by capacity. Then we extend this result to Minkowski sum of general random sets in $\mathbb Z^d$, including ranges of random walks and critical branching random walks, whose hitting probabilities are described by Newtonian capacity individually. |
| title | Minkowski sum of fractal percolation and random sets |
| topic | Probability 60G22, 60J05, 60K35 |
| url | https://arxiv.org/abs/2412.16415 |