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The threshold regime of finite volume bootstrap percolation

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  • Cerf, R.
  • Manzo, F.

Abstract

We prove that the threshold regime for bootstrap percolation in a d-dimensional box of diameter L with parameters p and l, where 3[less-than-or-equals, slant]l[less-than-or-equals, slant]d, is L~ exp°(l-1)(Cp-1/(d-l+1)), where exp°(l-1) is the exponential iterated l-1 times and C is bounded from above and from below by two positive constants depending on d, l only.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:101:y:2002:i:1:p:69-82
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    References listed on IDEAS

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    1. Adler, Joan, 1991. "Bootstrap percolation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 171(3), pages 453-470.
    2. Mountford, T. S., 1995. "Critical length for semi-oriented bootstrap percolation," Stochastic Processes and their Applications, Elsevier, vol. 56(2), pages 185-205, April.
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    Cited by:

    1. Mitsche, Dieter & Pérez-Giménez, Xavier & Prałat, Paweł, 2017. "Strong-majority bootstrap percolation on regular graphs with low dissemination threshold," Stochastic Processes and their Applications, Elsevier, vol. 127(9), pages 3110-3134.
    2. Blanquicett, Daniel, 2024. "The d-dimensional bootstrap percolation models with axial neighbourhoods," Stochastic Processes and their Applications, Elsevier, vol. 174(C).

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