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Bootstrap percolation

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  • Adler, Joan

Abstract

Bootstrap percolation (BP) models are systems where sites are initially randomly occupied. Those sites that do not maintain a suitable local environment of occupied sites are successively removed. This culling process can be identified with a cellular automation. Variations of the local rules concerning suitable environments, lead to different families of models, which have members with percolation transitions of the usual type, as well as representatives undergo different types of first order transitions. The latter transitions are manifestations of longer ranged phenomena in the systems. In this review different families of the BP type are introduced and their relationships summarized. The finite-size effects observed near the first order transitions are also discussed. Recent exact and numerical results are presented, and some applications and open problems are outlined.

Suggested Citation

  • Adler, Joan, 1991. "Bootstrap percolation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 171(3), pages 453-470.
    • Handle: RePEc:eee:phsmap:v:171:y:1991:i:3:p:453-470
    DOI: 10.1016/0378-4371(91)90295-N
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    Cited by:

    1. Kolotev, Sergei & Malyutin, Aleksandr & Burovski, Evgeni & Krashakov, Sergei & Shchur, Lev, 2018. "Dynamic fractals in spatial evolutionary games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 499(C), pages 142-147.
    2. Cerf, R. & Manzo, F., 2002. "The threshold regime of finite volume bootstrap percolation," Stochastic Processes and their Applications, Elsevier, vol. 101(1), pages 69-82, September.
    3. Gil, Maria Angeles & Gonzalez-Rodriguez, Gil & Colubi, Ana & Montenegro, Manuel, 2007. "Testing linear independence in linear models with interval-valued data," Computational Statistics & Data Analysis, Elsevier, vol. 51(6), pages 3002-3015, March.
    4. John Higgins & Tarun Sabarwal, 2021. "Control and Spread of Contagion in Networks," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202111, University of Kansas, Department of Economics.
    5. D. Dujak & A. Karač & Lj. Budinski-Petković & Z. M. Jakšić & S. B. Vrhovac, 2022. "Percolation and jamming properties in particle shape-controlled seeded growth model," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 95(9), pages 1-16, September.
    6. Franco Bagnoli & Emanuele Bellini & Emanuele Massaro & Raúl Rechtman, 2019. "Percolation and Internet Science," Future Internet, MDPI, vol. 11(2), pages 1-26, February.
    7. Mountford, T. S., 1995. "Critical length for semi-oriented bootstrap percolation," Stochastic Processes and their Applications, Elsevier, vol. 56(2), pages 185-205, April.
    8. Chen, Zhihua & An, Haizhong & An, Feng & Guan, Qing & Hao, Xiaoqing, 2018. "Structural risk evaluation of global gas trade by a network-based dynamics simulation model," Energy, Elsevier, vol. 159(C), pages 457-471.
    9. Bastas, N. & Giazitzidis, P. & Maragakis, M. & Kosmidis, K., 2014. "Explosive percolation: Unusual transitions of a simple model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 407(C), pages 54-65.

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