Threshold value of three dimensional bootstrap percolation

TL;DR

This paper investigates the critical probability p_c in three-dimensional bootstrap percolation, analyzing its behavior across different lattice sizes and its scaling limit as the lattice becomes infinite.

Contribution

It provides new insights into the scaling behavior of p_c in 3D bootstrap percolation and examines how it varies with lattice size.

Findings

p_c behavior varies with lattice size

scaling limit of p_c as lattice approaches infinity

quantitative estimates of p_c for different lattice lengths

Abstract

The following article deals with the critical value p_c of the three-dimensional bootstrap percolation. We will check the behavior of p_c for different lengths of the lattice and additionally we will scale p_c in the limit of an infinite lattice.