Locality approach to the bootstrap percolation paradox

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.

6 pages, 2 figures, 3 page supplemental material

References in corpus (17)

• Glassy dynamics of kinetically constrained models
• Exact Solution of a Jamming Transition: Closed Equations for a Bootstrap Percolation Problem
• Minimal contagious sets in random regular graphs
• Universality results for kinetically constrained spin models in two dimensions
• Clarification of the Bootstrap Percolation Paradox
• Nucleation and growth for the Ising model in $d$ dimensions at very low temperatures
• Sharp metastability threshold for an anisotropic bootstrap percolation model
• Explosive Percolation Obeys Standard Finite-Size Scaling in an Event-based Ensemble
• The second term for two-neighbour bootstrap percolation in two dimensions
• Refined universality for critical KCM: lower bounds
• Sharp threshold for the FA-2f kinetically constrained model
• Threshold value of three dimensional bootstrap percolation
• Compacted binary trees admit a stretched exponential
• Refined universality for critical KCM: upper bounds
• Finite-density effects in the Fredrickson-Andersen and Kob-Andersen kinetically-constrained models
• Sharp metastability transition for two-dimensional bootstrap percolation with symmetric isotropic threshold rules
• Sensitive bootstrap percolation second term