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]
  2. P. Antal and A. Pisztora, On the chemical distance for supercritical Bernoulli percolation. Ann. Probab. 24 (1996) 1036–1048. [CrossRef] [MathSciNet]
  3. D. Boivin, First passage percolation: the stationary case. Probab. Theory Related Fields 86 (1990) 491–499. [CrossRef] [MathSciNet]
  4. J.R. Brown, Ergodic theory and topological dynamics. Academic Press, Harcourt Brace Jovanovich Publishers, New York. Pure Appl. Math. 70 (1976).
  5. R.M. Burton and M. Keane, Density and uniqueness in percolation. Comm. Math. Phys. 121 (1989) 501–505. [CrossRef] [MathSciNet]
  6. J.T. Cox, The time constant of first-passage percolation on the square lattice. Adv. Appl. Probab. 12 (1980) 864–879. [CrossRef]
  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]
  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]
  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]
  10. O. Garet, Percolation transition for some excursion sets. Electron. J. Probab. 9 (2004) 255–292 (electronic). [MathSciNet]
  11. O. Häggström and R. Meester, Asymptotic shapes for stationary first passage percolation. Ann. Probab. 23 (1995) 1511–1522. [CrossRef] [MathSciNet]
  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.
  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]
  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]
  15. R. Marchand, Strict inequalities for the time constant in first passage percolation. Ann. Appl. Probab. 12 (2002) 1001–1038. [CrossRef] [MathSciNet]
  16. D. Richardson, Random growth in a tessellation. Proc. Cambridge Philos. Soc. 74 (1973) 515–528. [CrossRef] [MathSciNet]
  17. Y.G. Sinai, Introduction to ergodic theory. Princeton University Press, Princeton, N.J., Translated by V. Scheffer. Math. Notes 18 (1976).
  18. W.F. Stout, Almost sure convergence. Academic Press, A subsidiary of Harcourt Brace Jovanovich, Publishers, New York-London. Probab. Math. Statist. 24 (1974).
  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]

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.