Work

Sharp metastability transition for two-dimensional bootstrap percolation with symmetric isotropic threshold rules

Year: 2024

Type: article

Abstract: We study two-dimensional critical bootstrap percolation models. We establish that a class of these models including all isotropic threshold rules with a convex symmetric neighbourhood, undergoes a sharp metastability transition. This extends previous instances proved for several specific rules. The paper supersedes a draft by Alexander Holroyd and the first author from 2012. While it served a role in the subsequent development of bootstrap percolation universality, we have chosen to adopt a more contemporary viewpoint in its present form.

Source: Probability Theory and Related Fields

DOI: 10.1007/s00440-024-01310-3

Authors: Hugo Duminil-Copin, Ivailo Hartarsky

Institutions: University of Geneva, Institut des Hautes Études Scientifiques, TU Wien

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,990