Three‐Dimensional 2‐Critical Bootstrap Percolation: The Stable Sets Approach
Abstract
ABSTRACT Consider a ‐random subset of initially infected vertices in the discrete cube , and assume that the neighborhood of each vertex consists of the nearest neighbors in the ‐directions for each , where . Suppose we infect any healthy vertex already having infected neighbors, and that infected sites remain infected forever. In this article, we determine of the critical length for percolation up to a constant factor, for all with . We moreover give upper bounds for all remaining cases and believe that they are tight up to a constant factor.
Fields of Study & Subjects
Stochastic processes and statistical mechanics
Markov Chains and Monte Carlo Methods
Bayesian Methods and Mixture Models
Publication details
- Journal / source
- Random Structures and Algorithms
- Volume
- 68
- Issue
- 4
- Publication date
- 1 July 2026
- Language
- EN