article · 1997

Language Reference

Béla (-memp) Riordan

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Abstract

The critical probability for random Voronoi percolation in the plane is 1/2. (English summary) Probab. Theory Related Fields 136 (2006), no. 3, 417–468. This is a very good paper in which the result of the title is proven for Voronoĭ tessellations of a typical Poisson process in the plane. The main hurdle of extending Kesten’s famous result on bond percolation from the lattice Z 2 to this case is the absence of the Russo-Seymour-Welsh argument. The authors provide a slightly weaker statement which suffices for the proof, combined with sharp threshold results of E. Friedgut and G. Kalai [Proc. Amer. Math. Soc. 124 (1996), no. 10, 2993– 3002; MR1371123 (97e:05172)]. The paper is well written, and the authors have already extended their techniques and results to various related percolation models [Random Structures Algorithms 29 (2006), no. 4, 524–548; MR2268234 (2007h:60089)]. Reviewed by Aernout C. D. van Enter

Cite this paper

APA 7

Riordan, B. M. (1997). Language Reference.

MLA 9

Riordan, Béla (-memp). “Language Reference.” 1997.

Chicago

Riordan, Béla (-memp). 1997. “Language Reference.”

Harvard

Riordan, B.M. (1997) ‘Language Reference’.

BibTeX

@article{riordan1997language,
  title = {{Language Reference}},
  author = {Riordan, Béla (-memp)},
  year = {1997}
}

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