The Time of Bootstrap Percolation in High Dimensions
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912380011675648 |
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| author | Zhu, Fengxing |
| author_facet | Zhu, Fengxing |
| contents | We consider the $d$-neighbor bootstrap percolation process on the $d$-dimensional torus, with vertex set $V=\{1,\cdots,n\}^d$ and edge set $\{xy:\sum_{i=1}^d|x_i-y_i (\text{mod} \; n)|=1\}$. We determine the percolation time up to a constant factor with high probability when the initial infection probability is in a certain range and the infection threshold is $d$, extending one of the two main theorems from Balister,Bollob{á}s, and Smith (2016) about the percolation time with the infection threshold equal to $2$ on the two-dimensional torus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_11410 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Time of Bootstrap Percolation in High Dimensions Zhu, Fengxing Combinatorics Probability We consider the $d$-neighbor bootstrap percolation process on the $d$-dimensional torus, with vertex set $V=\{1,\cdots,n\}^d$ and edge set $\{xy:\sum_{i=1}^d|x_i-y_i (\text{mod} \; n)|=1\}$. We determine the percolation time up to a constant factor with high probability when the initial infection probability is in a certain range and the infection threshold is $d$, extending one of the two main theorems from Balister,Bollob{á}s, and Smith (2016) about the percolation time with the infection threshold equal to $2$ on the two-dimensional torus. |
| title | The Time of Bootstrap Percolation in High Dimensions |
| topic | Combinatorics Probability |
| url | https://arxiv.org/abs/2505.11410 |