Category: Statistics

Summary: Characterizing finite-size corrections to the activation threshold in k-neighbor bootstrap percolation on Erdos-Renyi graphs.

Bootstrap percolation studies cascading activation on random graphs: once enough neighbors are active, a node turns on as well. This experiment asks how the critical initial seed fraction for full activation approaches its large-system limit on Erdos-Renyi graphs, especially for k values beyond the best-studied two-neighbor case.

The simulation runs repeated activation processes across graph sizes and threshold values, estimates the critical seed fraction for each size, and then fits how that threshold approaches its asymptotic form. The focus is on the finite-size correction exponent rather than just the limiting threshold.

That finite-size scaling problem is important because practical systems are never infinite, and the correction rate may depend on k in a nontrivial way. The experiment aims to map that dependence systematically.

Method: Repeated bootstrap-percolation simulations on Erdos-Renyi graphs, followed by finite-size scaling fits of the critical seed fraction.

What is measured: Critical seed fraction by size, finite-size correction exponent, dependence on neighbor threshold k, and goodness of scaling fits.