Large deviations for subcritical bootstrap percolation on the random graph
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2017
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| _version_ | 1866908654825897984 |
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| author | Angel, Omer Kolesnik, Brett |
| author_facet | Angel, Omer Kolesnik, Brett |
| contents | We study atypical behavior in bootstrap percolation on the Erdős-Rényi random graph. Initially a set $S$ is infected. Other vertices are infected once at least $r$ of their neighbors become infected. Janson et al. (2012) locates the critical size of $S$, above which it is likely that the infection will spread almost everywhere. Below this threshold, a central limit theorem is proved for the size of the eventually infected set. In this note, we calculate the rate function for the event that a small set $S$ eventually infects an unexpected number of vertices, and identify the least-cost trajectory realizing such a large deviation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1705_06815 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Large deviations for subcritical bootstrap percolation on the random graph Angel, Omer Kolesnik, Brett Probability Combinatorics We study atypical behavior in bootstrap percolation on the Erdős-Rényi random graph. Initially a set $S$ is infected. Other vertices are infected once at least $r$ of their neighbors become infected. Janson et al. (2012) locates the critical size of $S$, above which it is likely that the infection will spread almost everywhere. Below this threshold, a central limit theorem is proved for the size of the eventually infected set. In this note, we calculate the rate function for the event that a small set $S$ eventually infects an unexpected number of vertices, and identify the least-cost trajectory realizing such a large deviation. |
| title | Large deviations for subcritical bootstrap percolation on the random graph |
| topic | Probability Combinatorics |
| url | https://arxiv.org/abs/1705.06815 |