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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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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DOI: https://doi.org/10.1007/s00440-007-0066-1
Mathematics Subject Classification (2000)
- 60K35
- 82B43