Infinite clusters in dependent automorphism invariant percolation on trees

Annals of Probability

Volumn 25, Issue 3, 1997, Pages 1423-1436

  Häggström, Olle ^a  

^a CHALMERS UNIVERSITY OF TECHNOLOGY   (Sweden)

Author keywords

Automorphism invariance; Branching number; Percolation; Topological ends; Trees

Indexed keywords

EID: 0040453578     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/aop/1024404518     Document Type: Article

References (19)

1. ADAMS, S. and LYONS, R. (1991). Amenability, Kazhdan's property, and percolation for trees, groups and equivalence relations. Israel J. Math. 75 341-370.
2. ALEXANDER, K. (1995). Percolation and minimal spanning forests in infinite graphs. Ann. Probab. 23 87-104.
3. BENJAMINI, I. and PERES, Y. (1994). Tree-indexed random walks on groups and first-passage percolation. Probab. Theory Related Fields 98 91-112.
4. BURTON, R. and KEANE, M. (1989). Density and uniqueness in percolation. Comm. Math. Phys. 121 501-505.
5. BURTON, R. and KEANE, M. (1991). Topological and metric properties of infinite clusters in stationary two-dimensional site percolation. Israel J. Math. 76 299-316.
6. DURRETT, R. (1991). Probability: Theory and Examples. Wadsworth and Brooks/Cole, Pacific Grove, CA.
7. GRIMMETT, G. (1994). Percolative problems. In Probability and Phase Transition (G. Grimmett, ed.) 69-86. Kluwer, Dordrecht.
8. HÄGGSTRÖM, O. (1996). The random-cluster model on a homogeneous tree. Probab. Theory Related Fields 104 231-253.
9. HÄGGSTRÖM, O. (1996). Uniform and minimal essential spanning forests on trees. Preprint.
10. HÄGGSTRÖM, O. (1996). Unpublished supplement.
11. KLEBANER, F. (1984). Geometric rate of growth in population size dependent branching processes. J. Appl. Probab. 21 40-49.
12. LYONS, R. (1990). Random walks and percolation on trees. Ann. Probab. 18 931-958.
13. LYONS, R. (1992). Random walks, capacity and percolation on trees. Ann. Probab. 20 2043-2088.
14. LYONS, R. and PEMANTLE, R. (1992). Random walk in random environment and first-passage percolation on trees. Ann. Probab. 20 125-136.
15. NEWMAN, C. M. (1995). A surface view of first-passage percolation. Proceedings of the 1994 International Congress of Mathematicians (S. D. Chatterji, ed.) 1017-1023. Birkhäuser, Boston.
16. NEWMAN, C. M. and SCHULMAN, L. S. (1981). Infinite clusters in percolation models. J. Statist. Phys. 26 613-628.
17. OLOFSSON, P. (1996). Branching processes with local dependencies. Ann. Appl. Probab. 6 238-268.
18. PEMANTLE, R. (1991). Choosing a spanning tree for the integer lattice uniformly. Ann. Probab. 19 1559-1574.
19. PEMANTLE, R. (1992). Automorphism invariant measures on trees. Ann. Probab. 20 1549-1566.