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arXiv · 1705.06815

Large deviations for subcritical bootstrap percolation on the random graph

Omer Angel·Brett Kolesnik
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Abstract

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.

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Omer Angel, Brett Kolesnik. 2021-01-05. Large deviations for subcritical bootstrap percolation on the random graph. https://doi.org/10.1007/s10955-021-02819-w

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