Unpredictable paths and percolation

Annals of Probability

Volumn 26, Issue 3, 1998, Pages 1198-1211

  Benjamini, Itai ^a   Pemantle, Robin ^b   Peres, Yuval ^c,d  

^a WEIZMANN INSTITUTE OF SCIENCE   (Israel)

^b UNIVERSITY OF WISCONSIN MADISON   (United States)

^c HEBREW UNIVERSITY OF JERUSALEM   (Israel)

^d UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Electrical networks; Multitype branching process; Percolation; Transience

Indexed keywords

EID: 0032388119     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/aop/1022855749     Document Type: Article

References (20)

1. ANTAL, P. and PISZTORA, A. (1996). On the chemical distance in supercritical Bernoulli percolation. Ann. Probab. 24 1036-1048.
2. ATHREYA, K. and NEY, P. (1972). Branching Processes. Springer, New York.
3. COX, T. and DURRETT, R. (1983). Oriented percolation in dimensions d ≥ 4; bounds and asymptotic formulas. Math. Proc. Cambridge Philos. Soc. 93 151-162.
4. DOYLE, P. G. and SNELL, E. J. (1984). Random Walks and Electrical Networks. Math. Assoc. Amer., Washington, D.C.
5. GRIMMETT, G. R. KESTEN, H. and ZHANG, Y. (1993). Random walk on the infinite cluster of the percolation model. Probab. Theory Related Fields 96 33-44.
6. GRIMMETT, G. R. and MARSTRAND, J. M. (1990). The supercritical phase of percolation is well behaved. Proc. Roy. Soc. London Ser. A 430 439-457.
7. HÄGGSTRÖM, O. MOSSEL, E. (1998). Nearest-neighbor walks with low predictability profile and percolation in 2 + ε dimensions. Ann. Probab. 26 1212-1231.
8. HIEMER, P. (1998). Dynamical renormalisation in oriented percolation. Preprint.
9. HOFFMAN, C. (1998). Unpredictable nearest neighbor processes. Preprint.
10. KESTEN, H. and STIGUM, B. P. (1966). Additional limit theorems for indecomposable multidimensional Galton-Watson processes. Ann. Math. Statist. 37 1463-1481.
11. KESTEN, H. and ZHANG, Y. (1990). The probability of a large finite cluster in supercritical Bernoulli percolation. Ann. Probab. 18 537-555.
12. LAWLER, G. (1991). Intersections of Random Walks. Birkhäuser, Boston.
13. LEVIN, D. and PERES, Y. (1998). Energy and cutsets in infinite percolation clusters. In Proceedings of the Cortona Workshop on Random Walks and Discrete Potential Theory (M. Picardello and W. Woess eds.). To appear.
14. LIGGETT, T. M. SCHONMANN, R. H. and STACEY, A. M. (1996). Domination by product measures. Ann. Probab. 24 1711-1726.
15. LYONS, R. (1990). Random walks and percolation on trees. Ann. Probab. 18 931-958.
16. LYONS, R. (1995). Random walks and the growth of groups. C. R. Acad. Sci. Paris 320 1361-1366.
17. MOORE, T. and SNELL, J. L. (1979). A branching process showing a phase transition. J. Appl. Probab. 16 252-260.
18. PEMANTLE, R. and PERES, Y. (1996). On which graphs are all random walks in random environments transient? In Random Discrete Structures (D. Aldous and R. Pemantle, eds.) 207-211. Springer, New York.
19. PISZTORA, A. (1996). Surface order large deviation for Ising, Potts and percolation models. Probab. Theory Related Fields 104 427-466.
20. SOARDI, P. M. 1994. Potential Theory on Infinite Networks. Springer, Berlin.