Bootstrap percolation, probabilistic cellular automata and sharpness
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2021
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910710724820992 |
|---|---|
| author | Hartarsky, Ivailo |
| author_facet | Hartarsky, Ivailo |
| contents | We establish new connections between percolation, bootstrap percolation, probabilistic cellular automata and deterministic ones. Surprisingly, 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 Toom on the stability of cellular automata w.r.t. noise and, inversely, how to deduce new results in bootstrap percolation universality from his work. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_01778 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Bootstrap percolation, probabilistic cellular automata and sharpness Hartarsky, Ivailo Probability Statistical Mechanics Cellular Automata and Lattice Gases 60K35 (Primary) 37B15, 60C05, 82B43, 82C20 (Secondary) We establish new connections between percolation, bootstrap percolation, probabilistic cellular automata and deterministic ones. Surprisingly, 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 Toom on the stability of cellular automata w.r.t. noise and, inversely, how to deduce new results in bootstrap percolation universality from his work. |
| title | Bootstrap percolation, probabilistic cellular automata and sharpness |
| topic | Probability Statistical Mechanics Cellular Automata and Lattice Gases 60K35 (Primary) 37B15, 60C05, 82B43, 82C20 (Secondary) |
| url | https://arxiv.org/abs/2112.01778 |