Percolation in a dependent random environment

Random Structures and Algorithms

Volumn 16, Issue 4, 2000, Pages 333-343

  Jonasson, Johan ^a   Mossel, Elchanan ^a   Peres, Yuval ^a  

^a CHALMERS UNIVERSITY OF TECHNOLOGY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034344104     PISSN: 10429832     EISSN: None     Source Type: Journal    
DOI: 10.1002/1098-2418(200007)16:4<333::AID-RSA3>3.0.CO;2-C     Document Type: Article

References (15)

1. T. Arak, P. Clifford, and D. Surgailis, Point-based polygonal models for random graphs, Adv Appl Probab 25 (1993), 348-372.
2. P.N. Balister, B. Bollobas, and A.M. Stacey, Dependent percolation in two dimensions, Probab Theory Related Fields, to appear.
3. I. Benjamini, R. Pemantle, and Y. Peres, Unpredictable paths and percolation, Ann Probab 26 (1998), 1198-1211.
4. M. Bramson, R. Durrett, and R.H. Schonmann, The contact process in a random environment, Ann Probab 19 (1991), 960-983.
5. T. Cox and R. Durrett, Oriented percolation in dimensions d > 4: bounds and asymptotic formulas, Math Proc Cambrige Philos Soc 93 (1983), 151-162.
6. P.G. Doyle, and E.J. Snell, Random walks and electrical networks, Carus Math Monographs 22 (1984).
7. G. Grimmett, Percolation, Springer-Verlag, New York, 1989.
8. G.R. Grimmett, H. Kesten, and Y. Zhang, Random walk on the infinite cluster of the percolation model. Probab Theory Related Fields 96 (1993), 33-44.
9. G. Grimmett, personal communication.
10. O. Häggström, Random-cluster representations in the study of phase transitions, Markov Proc Related Fields 4 (1998), 275-321.
11. O. Häggström, and E. Mossel, Nearest-neighbor walks with low predictability profile and percolation in 2 + ∈ dimensions, Ann Probab 26 (1998), 1212-1231.
12. A. Klein, "Multiscale analysis in disordered systems: percolation and contact process in random environments, " Probability and phase transition, Nato ASI Series, Kluwer Academic, Dordecht, 1994.
13. T. Liggett, The survival of one dimensional contact processes in random environments, Ann Probab 20 (1992), 696-723.
14. G. Nicholls, Spontaneous magnetization in the plane, Technical Report, University of Auckland, 1996.
15. P. Winkler, Dependent percolation and colliding random walks, Random Struct Alg 16(1) (2000), 58-84.