Boolean percolation on digraphs and random exchange processes
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arXiv
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866917840843440128 |
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| author | Braun, Georg |
| author_facet | Braun, Georg |
| contents | We study, in a general graph-theoretic formulation, a long-range percolation model introduced by Lamperti. For various underlying directed graphs, we discuss connections between this model and random exchange processes. We clarify, for $n \in \mathbb{N}$, under which conditions the lattices $\mathbb{N}_0^n$ and $\mathbb{Z}^n$ are essentially covered in this model. Moreover, for all $n \geq 2$, we establish that it is impossible to cover the directed $n$-ary tree in our model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_04772 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Boolean percolation on digraphs and random exchange processes Braun, Georg Probability 05C80, 60J80, 60K35, 82B43 We study, in a general graph-theoretic formulation, a long-range percolation model introduced by Lamperti. For various underlying directed graphs, we discuss connections between this model and random exchange processes. We clarify, for $n \in \mathbb{N}$, under which conditions the lattices $\mathbb{N}_0^n$ and $\mathbb{Z}^n$ are essentially covered in this model. Moreover, for all $n \geq 2$, we establish that it is impossible to cover the directed $n$-ary tree in our model. |
| title | Boolean percolation on digraphs and random exchange processes |
| topic | Probability 05C80, 60J80, 60K35, 82B43 |
| url | https://arxiv.org/abs/2111.04772 |