Locality approach to the bootstrap percolation paradox

TL;DR

This paper introduces a local approach to bootstrap percolation that reconciles previous discrepancies between simulations and theory, achieving high-accuracy predictions up to third-order asymptotics as infection probability diminishes.

Contribution

It presents a new local perspective that resolves longstanding discrepancies and enables precise predictions for bootstrap percolation behavior.

Findings

Excellent agreement between numerics and theory up to third-order expansion.

The new algorithm generates novel, accurate predictions for the model.

Reconciles Monte Carlo simulations with theoretical results.

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.