PreprintCC BY 4.0arXiv
Bootstrap percolation on the hypercube
Abstract
In this paper we obtain the critical probability pc(Qn,r) for bootstrap percolation with the infection threshold r=f(n)na on the n-dimensional hypercube Qn, where 0<a<1 and f(n)=no(1). More precisely, we obtain the exact first-order and second-order terms of pc(Qn,r) by extending the main theorem of Balogh, Bollob{á}s, and Morris (2009).
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BibTeX
@misc{zhu2026bootstrap,
title = {{Bootstrap percolation on the hypercube}},
author = {Fengxing Zhu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26615},
eprint = {2610.26615},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26615},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Bootstrap percolation on the hypercube
AU - Fengxing Zhu
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.26615
UR - https://arxiv.org/abs/2610.26615
AB - In this paper we obtain the critical probability p_c(Q_n,r) for bootstrap percolation with the infection threshold r=f(n)n^a on the n-dimensional hypercube Q_n, where 0<a<1 and f(n)=n^o(1). More precisely, we obtain the exact first-order and second-order terms of p_c(Q_n,r) by extending the main theorem of Balogh, Bollob{á}s, and Morris (2009).
ER -