The contact process on finite homogeneous trees

Probability Theory and Related Fields

Volumn 121, Issue 4, 2001, Pages 551-576

  Stacey, Alan ^a  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

Contact process; Finite; Tree

Indexed keywords

EID: 0035730804     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s004400100149     Document Type: Article

References (23)

1. Barlow, R.E., Proschan, F.: Mathematical theory of reliability, Wiley, New York 1965
2. Bezuidenhout. C., Grimmett, G.: The critical contact process dies out, Annals of Probability, 18, 1462-1482 (1990)
3. Chen, J.W.: The contact process on a finite system in higher dimensions, Chinese Journal of Contemporary Mathematics, 15, 13-20 (1994)
4. Cox, D.R., Miller, H.D.: The theory of stochastic processes, Chapman and Hall, London 1965
5. Durrett, R., Liu, X.: The contact process on a finite set, Annals of Probability, 16, 1158-1173 (1988)
6. Durrett, R., Schonmann, R.H.: The contact process on a finite set II, Annals of Probability, 16, 1570-1583 (1988)
7. Durrett, R., Schonmann, R.H., Tanaka, N.: The contact process on a finite set III: the critical case. Annals of Probability, 17, 1303-1321 (1989)
8. Harris, T.E.: Contact interactions on a lattice. Annals of Probability, 2, 969-988 (1974)
9. Lalley, S.: Growth profile and invariant measures for the weakly supercritical contact process on a homogeneous tree, Annals of Probability, 27, 206-225 (1999)
10. Lalley, S., Sellke, T.: Limit set of a weakly supercritical contact process on a homogeneous tree, Annals of Probability, 26, 644-657 (1998)
11. Liggett, T.M.: Interacting particle systems, Springer-Verlag, New York-Berlin 1985
12. Liggett, T.M.: Branching random walks and contact processes on homogeneous trees, Probability Theory and Related Fields, 106, 495-519 (1996)
13. Liggett, T.M.: Multiple transition points for the contact process on the binary tree, Annals of Probability, 24, 1675-1710 (1996)
14. Liggett, T.M.: Stochastic interacting systems: Contact, voter and exclusion processes, Springer-Verlag, New York-Berlin 1999
15. Madras, N., Schinazi, R.: Branching random walks on trees. Stochastic Processes and their Applications, 42, 255-267 (19)
16. Morrow, G., Schinazi, R., Zhang, Y.: The critical contact process on a homogeneous tree, Journal of Applied Probability, 31, 250-255 (1994)
17. Mountford, T.S.: A metastable result for the finite multidimensional contact process, Canadian Mathematical Bulletin, 36, 216-226 (1993)
18. Pemantle, R.: The contact process on trees, Annals of Probability, 20, 2089-2116 (1992)
19. Pemantle, R., Stacey, A.M.: The branching random walk and contact process on Galton-Walson and non-homogeneous trees. Annals of Probability, 2001, to appear
20. Salzano, M., Schonmann, R.H.: A new proof that for the contact process on homogeneous trees, local survival implies complete convergence. Annals of Probability, 26, 1251-1258 (1998)
21. Schonmann, R.H.: The triangle condition for contact processes on homogeneous trees, Journal of Statistical Physics, 90, 1429-1440 (1998)
22. Stacey, A.M.: Partial immunization processes, in preparation
23. Stacey, A.M.: The existence of an intermediate phase for the contact process on trees, Annals of Probability, 24, 1711-1726 (1996)