Free Access
Volume 8, August 2004
Page(s) 169 - 199
Published online 15 September 2004
  1. M. Aizenman, H. Kesten and C.M. Newman, Uniqueness of the infinite cluster and continuity of connectivity functions for short and long range percolation. Comm. Math. Phys. 111 (1987) 505–531. [CrossRef] [MathSciNet] [Google Scholar]
  2. P. Antal and A. Pisztora, On the chemical distance for supercritical Bernoulli percolation. Ann. Probab. 24 (1996) 1036–1048. [CrossRef] [MathSciNet] [Google Scholar]
  3. D. Boivin, First passage percolation: the stationary case. Probab. Theory Related Fields 86 (1990) 491–499. [CrossRef] [MathSciNet] [Google Scholar]
  4. J.R. Brown, Ergodic theory and topological dynamics. Academic Press, Harcourt Brace Jovanovich Publishers, New York. Pure Appl. Math. 70 (1976). [Google Scholar]
  5. R.M. Burton and M. Keane, Density and uniqueness in percolation. Comm. Math. Phys. 121 (1989) 501–505. [CrossRef] [MathSciNet] [Google Scholar]
  6. J.T. Cox, The time constant of first-passage percolation on the square lattice. Adv. Appl. Probab. 12 (1980) 864–879. [CrossRef] [Google Scholar]
  7. J.T. Cox and R. Durrett, Some limit theorems for percolation processes with necessary and sufficient conditions. Ann. Probab. 9 (1981) 583–603. [CrossRef] [MathSciNet] [Google Scholar]
  8. J.T. Cox and H. Kesten, On the continuity of the time constant of first-passage percolation. J. Appl. Probab. 18 (1981) 809–819. [CrossRef] [MathSciNet] [Google Scholar]
  9. R. Durrett and T.M. Liggett, The shape of the limit set in Richardson's growth model. Ann. Probab. 9 (1981) 186–193. [CrossRef] [MathSciNet] [Google Scholar]
  10. O. Garet, Percolation transition for some excursion sets. Electron. J. Probab. 9 (2004) 255–292 (electronic). [MathSciNet] [Google Scholar]
  11. O. Häggström and R. Meester, Asymptotic shapes for stationary first passage percolation. Ann. Probab. 23 (1995) 1511–1522. [CrossRef] [MathSciNet] [Google Scholar]
  12. J.M. Hammersley and D.J.A. Welsh, First-passage percolation, subadditive processes, stochastic networks, and generalized renewal theory, in Proc. Internat. Res. Semin., Statist. Lab., Univ. California, Berkeley, Calif., Springer-Verlag, New York (1965) 61–110. [Google Scholar]
  13. H. Kesten, Aspects of first passage percolation, in École d'été de probabilités de Saint-Flour, XIV–1984, Springer, Berlin. Lect. Notes Math. 1180 (1986) 125–264. [CrossRef] [Google Scholar]
  14. H. Kesten and Y. Zhang, The probability of a large finite cluster in supercritical Bernoulli percolation. Ann. Probab. 18 (1990) 537–555. [CrossRef] [MathSciNet] [Google Scholar]
  15. R. Marchand, Strict inequalities for the time constant in first passage percolation. Ann. Appl. Probab. 12 (2002) 1001–1038. [CrossRef] [MathSciNet] [Google Scholar]
  16. D. Richardson, Random growth in a tessellation. Proc. Cambridge Philos. Soc. 74 (1973) 515–528. [CrossRef] [MathSciNet] [Google Scholar]
  17. Y.G. Sinai, Introduction to ergodic theory. Princeton University Press, Princeton, N.J., Translated by V. Scheffer. Math. Notes 18 (1976). [Google Scholar]
  18. W.F. Stout, Almost sure convergence. Academic Press, A subsidiary of Harcourt Brace Jovanovich, Publishers, New York-London. Probab. Math. Statist. 24 (1974). [Google Scholar]
  19. J. van den Berg and H. Kesten, Inequalities for the time constant in first-passage percolation. Ann. Appl. Probab. 3 (1993) 56–80. [CrossRef] [MathSciNet] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.