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arXiv · 2412.20982

Bootstrap percolation on a generalized Hamming cube

Fengxing Zhu
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Abstract

We consider the $r$-neighbor bootstrap percolation process on the graph with vertex set $V=\{0,1\}^n$ and edges connecting the pairs at Hamming distance $1,2,\dots,k$, where $k\ge 2$. We find asymptotics of the critical probability of percolation for $r=2,3$. In the deterministic setting, we obtain several results for the size of the smallest percolating set for $k\ge 2$.

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Fengxing Zhu. 2026-03-25. Bootstrap percolation on a generalized Hamming cube. https://arxiv.org/abs/2412.20982

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