Finite-size effects for anisotropic bootstrap percolation: logarithmic corrections

TL;DR

This paper investigates finite-size effects in an anisotropic bootstrap percolation model, providing bounds and discussing similarities with related models to understand critical behavior in finite systems.

Contribution

It offers new bounds on finite-size effects in anisotropic bootstrap percolation and compares these with semi-oriented models, advancing understanding of finite system behavior.

Findings

Established upper and lower bounds on finite-size effects

Identified similarities with semi-oriented bootstrap percolation

Enhanced understanding of anisotropic bootstrap percolation dynamics

Abstract

In this note we analyze an anisotropic, two-dimensional bootstrap percolation model introduced by Gravner and Griffeath. We present upper and lower bounds on the finite-size effects. We discuss the similarities with the semi-oriented model introduced by Duarte.