Shape theorem and surface fluctuation for Poisson cylinders
| Autor: | Hilario, Marcelo, Li, Xinyi, Panov, Petr |
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| Rok vydání: | 2018 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In this work, we prove a shape theorem for Poisson cylinders and give a power law bound on surface fluctuations. We prove that for any $a \in (1/2, 1)$, conditioned on the origin being in the set of cylinders, every point in this set, whose Euclidean norm is less than $R$, lies at an internal distance less than $R+O(R^a)$ from the origin. Comment: 19 pages, 3 figures |
| Databáze: | arXiv |
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