Summary
We prove that if the complete convergence theorem holds for the basic contact process in dimension d with infection parameter λ larger than the critical value in this dimension, then the same theorem holds for this process in any dimension d’ > d for any λ’ > λ.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
R. Durrett (1980) — On the growth of the one dimensional contact processes. Ann. Probab. 8, 890–907
R. Durrett (1984) — Oriented percolation in two dimensions. Ann. Probab. 12, 999–1040
R. Durrett (1985) — Stochastic growth models: ten problems for the 80’s (and 90’s). Contemporary Mathematics 41, 87–99
R. Durrett, D. Griffeath (1982) — Contact processes in several dimensions. Z. Wahrsch. Verw. Gebiete 59, 535–552
D. Griffeath (1978) — Limit theorems for nonergodic set valued Markov processes. Ann. Probab. 6, 379–387.
D. Griffeath (1979) — Additive and Cancelative Interacting Particle Systems. Springer Lecture Notes in Mathematics, vol. 724.
D. Griffeath (1981) — The basic contact process. Stochastic Process Appl. 11, 151–186
T.E. Harris (1974) — Contact interactions on a lattice. Ann. Probab. 2, 969–988
T.E. Harris (1976) — On a class of set-valued Markov processes. Ann. Probab. 4, 175–194
T.M. Liggett (1978) — Attractive nearest-neighbor spin systems on the integers. Ann. Probab. 6, 629–636
T.M. Liggett (1985) — Interacting Particle Systems. Springer Verlag
R.H. Schonmann (1986a) — A new proof of the complete convergence theorem for contact processes in several dimensions with large infection parameter. Ann. Probab. (to appear)
R.H. Schonmann (1986b) — The asymmetric contact process. J. Statistical Physics (to appear)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1987 Springer-Verlag New York, Inc.
About this chapter
Cite this chapter
Schonmann, R.H. (1987). A New Look at Contact Processes in Several Dimensions. In: Kesten, H. (eds) Percolation Theory and Ergodic Theory of Infinite Particle Systems. The IMA Volumes in Mathematics and Its Applications, vol 8. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8734-3_15
Download citation
DOI: https://doi.org/10.1007/978-1-4613-8734-3_15
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4613-8736-7
Online ISBN: 978-1-4613-8734-3
eBook Packages: Springer Book Archive