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- Title
Some toy models of self-organized criticality in percolation.
- Authors
Cerf, Raphaël; Forien, Nicolas
- Abstract
We consider the Bernoulli percolation model in a finite box and we introduce an automatic control of the percolation parameter, which is a function of the percolation configuration. For a suitable choice of this automatic control, the model is self-critical, i.e., the percolation parameter converges to the critical point pc when the size of the box tends to infinity. We study here three simple examples of such models, involving the size of the largest cluster, the number of vertices connected to the boundary of the box, or the distribution of the cluster sizes.
- Subjects
BINOMIAL distribution; PERCOLATION theory; CONFIGURATIONS (Geometry); AUTOMATIC control systems; GEOMETRIC vertices
- Publication
ALEA. Latin American Journal of Probability & Mathematical Statistics, 2022, Vol 19, Issue 1, p367
- ISSN
1980-0436
- Publication type
Article
- DOI
10.30757/ALEA.v19-14