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Scaling and Inverse Scaling in Anisotropic Bootstrap Percolation

  • Aernout C. D. van EnterEmail author
Chapter
Part of the Emergence, Complexity and Computation book series (ECC, volume 27)

Abstract

In bootstrap percolation, it is known that the critical percolation threshold tends to converge slowly to zero with increasing system size, or, inversely, the critical size diverges fast when the percolation probability goes to zero. To obtain higher-order terms (i.e. sharp and sharper thresholds) for the percolation threshold in general is a hard question. In the case of two-dimensional anisotropic models, sometimes such correction terms can be obtained from inversion in a relatively simple manner.

Keywords

Bootstrap percolation Anisotropic Unbalanced Inversion Percolation threshold 

Notes

Acknowledgements

I thank the organisers for their invitation to talk at the 2013 EURANDOM meeting on Probabilistic Cellular Automata, and I thank my colleagues and co-workers, Joan Adler, Jose Duarte, Hugo Duminil-Copin, Anne Fey-den Boer, Tim Hulshof and Rob Morris, as well as Susan Boerma-Klooster and Roberto Schonmann, for all they taught me. I thank Rob Morris for correcting me on the (1, b)-constant. Moreover, I thank Tim Hulshof for helpful advice on the manuscript.

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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Johann Bernoulli Institute for Mathematics and Computer ScienceUniversity of GroningenGroningenThe Netherlands

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