Euclidean models of first-passage percolation

Probability Theory and Related Fields

Volumn 108, Issue 2, 1997, Pages 153-170

  Howard, C Douglas ^a   Newman, Charles M ^b  

^a POLYTECHNIC UNIVERSITY   (United States)

^b NEW YORK UNIVERSITY   (United States)

Author keywords

First passage percolation; Geodesic; Poisson process; Shape theorem; Voronoi tesselation

Indexed keywords

EID: 0031532659     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s004400050105     Document Type: Article

References (20)

1. Aizenman, M.: Scaling limit for the incipient spanning clusters (preprint 1996)
2. Benjamini, I., Schramm, O.: Conformal invariance of Voronoi percolation (preprint 1996)
3. Cox, J.T., Durrett, R. Some limit theorems for percolation processes with necessary and sufficient conditions, Ann. Prob. 9, 583-603 (1981)
4. Durrett, R., Liggett, T.M.: The shape of the limit set in Richardson's growth model, Ann. Prob. 9, 186-193 (1981)
5. Hammersley, J.M., Welsh, D.J.A.: First-passage percolation, subadditive processes, stochastic networks and generalized renewal theory, Bernoulli, Bayes, Laplace Anniversary Volume (J. Neyman and L. LeCam, eds.), Springer, Berlin, pp. 61-110 (1965)
6. Kesten, H.: Aspects of first-passage percolation, Lecture Notes in Mathematics, vol. 1180, Springer, Berlin, pp. 125-264 (1986)
7. Kesten, H.: On the speed of convergence in first-passage percolation, Ann. Appl. Probab. 3, 296-338 (1993)
8. Liggett, T.M.: Interacting Particle Systems, Springer, New York, 1985
9. Licea, C., Newman, C.M.: Geodesics in two-dimensional first-passage percolation, Ann. Prob. 24, 399-410 (1996)
10. Licea, C., Newman, C.M., Piza, M.S.T.: Superdiffusivily in first-passage percolation, Prob. Theory Rel. Fields 106, 559-591 (1996)
11. Nagaev, S.V.: Large deviations of sums of independent random variables, Ann. Prob. 7, 745-789 (1979)
12. Newman, C.M.: A Surface View of First-Passage Percolation, Proceedings of the International Congress of Mathematicians (S.D. Chatterji, ed.), Birkhäuser, Basel, pp. 1017-1023 (1995)
13. Newman, C.M., Piza, M.S.T.: Divergence of shape fluctuations in two dimensions, Ann. Prob. 23, 977-1005 (1995)
14. Richardson, D.: Random growth in a tesselalion, Proc. Cambridge Philos. Soc. 74, 515-528 (1973)
15. Sznitman, A.-S.: Distance fluctuations and Lyapunov exponents. Ann. Prob. 24, 1504-1530 (1996)
16. Vahidi-Asl, M.Q., Wierman, J.C.: First-passage percolation on the Voronoi tessellation and Delaunay triangulation. Random Graphs '87 (M. Karoński, J. Jaworski and A. Ruciński, ed.), Wiley, New York, pp. 341-359 (1990)
17. Vahidi-Asl, M.Q., Wierman, J.C.: A shape result for first-passage percolation on the Voronoi tessellation and Delaunay triangulation, Random Graphs '89 (A. Frieze and T. Łuczak, ed.), Wiley, New York, pp. 247-262 (1992)
18. Zerner, M.P.W.: private communication
19. Znev, S.A., Sidorenko, A.F.: Continuous models of percolation theory I, Theoretical and Mathematical Physics 62, 76-86 (1985) (51-58 in translation from Russian)
20. Zuev, S.A., Sidorenko, A.F.: Continuous models of percolation theory II, Theoretical and Mathematical Physics 62, 253-262 (1985) (171-177 in translation from Russian)