Percolation on random Johnson–Mehl tessellations and related models |
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Authors: | Béla Bollobás Oliver Riordan |
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Institution: | (1) Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WB, UK;(2) Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, USA |
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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.
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. |
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Keywords: | 60K35 82B43 |
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