Percolation on stationary tessellations: models, mean values, and second-order structure
نویسندگان
چکیده
منابع مشابه
Erratum: Percolation on random Johnson–Mehl tessellations and related models
The proof presented in [2] of the result that the critical probability for percolation on a random Johnson–Mehl tessellation is 1/2 contains a (glaring!) error; we are very grateful to Rob van den Berg for bringing this to our attention. Fortunately, the error is easy to correct; as is often the case when one applies sharp-threshold results such as those of Talagrand [6] or Friedgut and Kalai [...
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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 twodimensional slices of higher-dimensional Voronoi tessellations. Surprisingly, the proof is a little simpler for these more complicated models.
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It is known that, for site percolation on the Cayley graph of a cocompact Fuchsian group of genus ≥ 2, infinitely many infinite connected clusters exist almost surely for certain values of the parameter p = P{site is open}. In such cases, the set Λ of limit points at ∞ of an infinite cluster is a perfect, nowhere dense set of Lebesgue measure 0. In this paper, a variational formula for the Haus...
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There are various models of first passage percolation (FPP) in R. We want to start a very general study of this topic. To this end we generalize the first passage percolation model on the lattice Z to R and adapt the results of [Boi90] to prove a shape theorem for ergodic random pseudometrics on R. A natural application of this result will be the study of FPP on random tessellations where a flu...
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CHRISTIAN PIGORSCH and ROBERT STELZER Institute of Econometrics and Operations Research, Department of Economics, University of Bonn, Adenauerallee 24-42, D-53113 Bonn, Germany. E-mail: [email protected] Zentrum Mathematik & TUM Institute for Advanced Study, Technische Universität München, Boltzmannstraße 3, D-85747 Garching, Germany. E-mail: [email protected], url: http://www-m4....
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ژورنال
عنوان ژورنال: Journal of Applied Probability
سال: 2014
ISSN: 0021-9002,1475-6072
DOI: 10.1239/jap/1417528483