The PDF file you selected should load here if your Web browser has a PDF reader plug-in installed (for example, a recent version of Adobe Acrobat Reader).

Alternatively, you can also download the PDF file directly to your computer, from where it can be opened using a PDF reader. To download the PDF, click the Download link below.

If you would like more information about how to print, save, and work with PDFs, Highwire Press provides a helpful Frequently Asked Questions about PDFs.

Download this PDF file Fullscreen Fullscreen Off

References

  • Addario-Berry, L. and Sarkar, A. (2005). The simple random walk on a random voronoi tiling. Available at URL.
  • Broutin, N. (2010). Private communication.
  • Calka, Pierre. Precise formulae for the distributions of the principal geometric characteristics of the typical cells of a two-dimensional Poisson-Voronoi tessellation and a Poisson line process. Adv. in Appl. Probab. 35 (2003), no. 3, 551--562. MR1990603
  • Cox, J. Theodore; Gandolfi, Alberto; Griffin, Philip S.; Kesten, Harry. Greedy lattice animals. I. Upper bounds. Ann. Appl. Probab. 3 (1993), no. 4, 1151--1169. MR1241039
  • Fontes, Luiz; Newman, Charles M. First passage percolation for random colorings of ${\bf Z}^ d$. Ann. Appl. Probab. 3 (1993), no. 3, 746--762. MR1233623
  • Grimmett, Geoffrey. Percolation. Springer-Verlag, New York, 1989. xii+296 pp. ISBN: 0-387-96843-1 MR0995460
  • Hammersley, J. M.; Welsh, D. J. A. First-passage percolation, subadditive processes, stochastic networks, and generalized renewal theory. 1965 Proc. Internat. Res. Semin., Statist. Lab., Univ. California, Berkeley, Calif. pp. 61--110 Springer-Verlag, New York MR0198576
  • Houdré, C. and Privault, N. (2003). Surface measures and related functional inequalities on configuration spaces. Technical report, Université de La Rochelle. Prépublication 2003-04. Available at URL.
  • Howard, C. Douglas. Models of first-passage percolation. Probability on discrete structures, 125--173, Encyclopaedia Math. Sci., 110, Springer, Berlin, 2004. MR2023652
  • Kesten, Harry. Aspects of first passage percolation. École d'été de probabilités de Saint-Flour, XIV—1984, 125--264, Lecture Notes in Math., 1180, Springer, Berlin, 1986. MR0876084
  • Kesten, Harry. On the speed of convergence in first-passage percolation. Ann. Appl. Probab. 3 (1993), no. 2, 296--338. MR1221154
  • Liggett, T. M.; Schonmann, R. H.; Stacey, A. M. Domination by product measures. Ann. Probab. 25 (1997), no. 1, 71--95. MR1428500
  • Pimentel, Leandro P. R. Asymptotics for first-passage times on Delaunay triangulations. Combin. Probab. Comput. 20 (2011), no. 3, 435--453. MR2784636
  • Pimentel, L. P. R. (2010). On some fundamental aspects of polyominoes on random Voronoi tilings. Accepted for publication by the Braz. J. of Probab. Stat.. Available at URL.
  • Vahidi-Asl, Mohammad Q.; Wierman, John C. First-passage percolation on the Voronoĭ tessellation and Delaunay triangulation. Random graphs '87 (Poznań, 1987), 341--359, Wiley, Chichester, 1990. MR1094141
Bookmark and Share


Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.