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Scaling and Inverse Scaling in Anisotropic Bootstrap Percolation

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Probabilistic Cellular Automata

Part of the book series: Emergence, Complexity and Computation ((ECC,volume 27))

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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.

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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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  1. Johann Bernoulli Institute for Mathematics and Computer Science, University of Groningen, P.O. Box 407, 9700 AK, Groningen, The Netherlands

    Aernout C. D. van Enter

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Correspondence to Aernout C. D. van Enter .

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  1. Laboratoire de Mathématiques et Applications UMR 7348, Université de Poitiers, CNRS, Poitiers, France

    Pierre-Yves Louis

  2. University of Technology, Eindhoven, Noord-Brabant, The Netherlands

    Francesca R. Nardi

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van Enter, A.C.D. (2018). Scaling and Inverse Scaling in Anisotropic Bootstrap Percolation. In: Louis, PY., Nardi, F. (eds) Probabilistic Cellular Automata. Emergence, Complexity and Computation, vol 27. Springer, Cham. https://doi.org/10.1007/978-3-319-65558-1_5

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  • DOI: https://doi.org/10.1007/978-3-319-65558-1_5

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