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Probabilistic Cellular AutomataScaling and Inverse Scaling in Anisotropic Bootstrap Percolation

Probabilistic Cellular Automata: Scaling and Inverse Scaling in Anisotropic Bootstrap Percolation [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.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Probabilistic Cellular AutomataScaling and Inverse Scaling in Anisotropic Bootstrap Percolation

Part of the Emergence, Complexity and Computation Book Series (volume 27)
Editors: Louis, Pierre-Yves; Nardi, Francesca R.
van Enter, Aernout C. D.
Probabilistic Cellular Automata — Feb 22, 2018
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Publisher
Springer International Publishing
Copyright
© Springer International Publishing AG 2018
ISBN
978-3-319-65556-7
Pages
69 –77
DOI
10.1007/978-3-319-65558-1_5
Publisher site
See Chapter on Publisher Site

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.]

Published: Feb 22, 2018

Keywords: Bootstrap percolation; Anisotropic; Unbalanced; Inversion; Percolation threshold

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