# Bootstrap Percolation, Probabilistic Cellular Automata and Sharpness

@article{Hartarsky2022BootstrapPP, title={Bootstrap Percolation, Probabilistic Cellular Automata and Sharpness}, author={Ivailo Hartarsky}, journal={Journal of Statistical Physics}, year={2022} }

We establish new connections between percolation, bootstrap percolation, probabilistic cellular automata and deterministic ones. Sur-prisingly, by juggling with these in various directions, we eﬀortlessly obtain a number of new results in these ﬁelds. In particular, we prove the sharpness of the phase transition of attractive absorbing probabilistic cellular automata, a class of bootstrap percolation models and kinetically constrained models. We further show how to recover a classical result of…

## 2 Citations

### On a class of probabilistic cellular automata with size-$3$ neighbourhood and their applications in percolation games

- Mathematics
- 2022

A BSTRACT . Different versions of percolation games on Z 2 , with parameters p and q that indicate, respectively, the probability with which a site in Z 2 is labeled a trap and the probability with…

### Subcritical bootstrap percolation via Toom contours

- MathematicsElectronic Communications in Probability
- 2022

In this note we provide an alternative proof of the fact that subcritical bootstrap percolation models have a positive critical probability in any dimension. The proof relies on a recent extension…

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