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Percolation on random Johnson–Mehl tessellations and related models
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  • Published: 15 March 2007

Percolation on random Johnson–Mehl tessellations and related models

  • Béla Bollobás1,2 &
  • Oliver Riordan1 

Probability Theory and Related Fields volume 140, pages 319–343 (2008)Cite this article

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An Erratum to this article was published on 31 October 2009

Abstract

We make use of the recent proof that the critical probability for percolation on random Voronoi tessellations is 1/2 to prove the corresponding result for random Johnson–Mehl tessellations, as well as for two-dimensional slices of higher-dimensional Voronoi tessellations. Surprisingly, the proof is a little simpler for these more complicated models.

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Authors and Affiliations

  1. Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WB, UK

    Béla Bollobás & Oliver Riordan

  2. Department of Mathematical Sciences, University of Memphis, Memphis, TN, 38152, USA

    Béla Bollobás

Authors
  1. Béla Bollobás
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  2. Oliver Riordan
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Corresponding author

Correspondence to Oliver Riordan.

Additional information

B. Bollobás’s research was supported in part by NSF grants CCR-0225610 and DMS-0505550 and ARO grant W911NF-06-1-0076. O. Riordan’s research was supported by a Royal Society Research Fellowship.

An erratum to this article can be found online at http://dx.doi.org/10.1007/s00440-009-0247-1.

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Bollobás, B., Riordan, O. Percolation on random Johnson–Mehl tessellations and related models. Probab. Theory Relat. Fields 140, 319–343 (2008). https://doi.org/10.1007/s00440-007-0066-1

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  • Received: 24 October 2006

  • Revised: 16 February 2007

  • Published: 15 March 2007

  • Issue Date: March 2008

  • DOI: https://doi.org/10.1007/s00440-007-0066-1

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Mathematics Subject Classification (2000)

  • 60K35
  • 82B43
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