English

Locality approach to the bootstrap percolation paradox

Statistical Mechanics 2025-12-16 v1 Probability

Abstract

We revisit the Bootstrap Percolation model, leveraging recent mathematical advances linking it with its local counterpart. This new perspective resolves, for the first time, historic discrepancies between Monte Carlo simulations and theoretical results: previously, those predictions disagreed even in the first-order asymptotics of the model. In contrast, our framework achieves excellent agreement between numerics and theory, which now match up to the third-order expansion, as the infection probability approaches zero. Our algorithm allows us to generate novel predictions for the model.

Cite

@article{arxiv.2410.01619,
  title  = {Locality approach to the bootstrap percolation paradox},
  author = {Ivailo Hartarsky and Augusto Teixeira},
  journal= {arXiv preprint arXiv:2410.01619},
  year   = {2025}
}

Comments

6 pages, 2 figures, 3 page supplemental material

R2 v1 2026-06-28T19:05:22.726Z