Janko Gravner

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math.PR2025

Two-stage Bootstrap Percolation

Zihao Fang, Janko Gravner, David Sivakoff

We introduce and study two variants of two-stage growth dynamics in $Z^{2}$ with state space ${0, 1, 2}^{Z^{2}}$ . In each variant, vertices in state $0$ can be change…

math.PR2025

Polluted Modified Bootstrap Percolation

Janko Gravner, Alexander Holroyd, Sangchul Lee +1

In the polluted modified bootstrap percolation model, sites in the square lattice are independently initially occupied with probability $p$ or closed with probability $q$ . A site b…