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Rates for the probability of large cubes being non-internally spanned in modified bootstrap percolation
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  • Published: June 1992

Rates for the probability of large cubes being non-internally spanned in modified bootstrap percolation

  • T. S. Mountford1 

Probability Theory and Related Fields volume 93, pages 159–167 (1992)Cite this article

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  • 8 Citations

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Summary

We find the exact rate of decay for the probability that a large cube is not internally spanned for the modified bootstrap percolation. It is proven that for cubes of large side the event that the cube is not internally spanned is essentially the same as the event that the cube possesses a completely vacant line.

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References

  • Andjel., E.: Critical exponents for 2-dimensional bootstrap percolation. Ann. Probab. (to appear)

  • Andjel, E.: Mountford, T.S., Schonmann, R.: Equivalence of exponential decay rates for bootstrap percolation-like cellular automata, 1991

  • Aizenmann, M., Lebowitz, J.L.: Metastability effects in bootstrap percolation. J. Phys. A Math. Gen.21, 3801–3813 (1988)

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  • van Enter, A.C.D.: Proof of Straley's argument for bootstrap percolation. J. Stat., Phys.48, 943–945 (1987)

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  • Schonmann, R.: On the behaviour of some cellular automata related to bootstrap percolation. Ann. Probab. (to appear)

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of California, 90024, Los Angeles, CA, USA

    T. S. Mountford

Authors
  1. T. S. Mountford
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Additional information

Research partially supported by NSF DMS 9157461 and a grant from the Sloan Foundation

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Cite this article

Mountford, T.S. Rates for the probability of large cubes being non-internally spanned in modified bootstrap percolation. Probab. Th. Rel. Fields 93, 159–167 (1992). https://doi.org/10.1007/BF01195227

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  • Received: 13 June 1991

  • Revised: 03 February 1992

  • Issue Date: June 1992

  • DOI: https://doi.org/10.1007/BF01195227

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Mathematics Subject Classification

  • 60 K 35
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