Abstract
We prove that the Harris contact process shows metastable behavior for any supercritical value of the parameter, even when some macroscopic observables are observed.
Similar content being viewed by others
References
M. Cassandro, A. Galves, E. Olivieri, and M. E. Vares, Metastable behavior of stochastic dynamics: A pathwise approach,J. Stat. Phys. 35:603 (1984).
R. Durrett and D. Griffeath, Supercritical contact processes on ℤ,Ann. Prob. 8:890 (1980).
D. Griffeath,Additive and Cancelative Interacting Particle Systems (Lecture Notes in Mathematics No. 724, Springer, New York).
D. Griffeath, The basic contact processes,Stoch. Proc. Appl. 11:151 (1981).
O. Penrose and J. L. Lebowitz, Towards a rigorous molecular theory of metastability, inFluctuation Phenomena, E. W. Montroll and J. L. Lebowitz, eds. (North-Holland, Amsterdam, 1979).
G. L. Sewell, Stability, equilibrium and metastability in statistical mechanics,Phys. Rep. 57:307 (1980).
P. Grassberger and A. de la Torre, Reggeon field theory (Schlögl first model) on a lattice: Monte Carlo calculations of critical behavior,Ann. Phys. (N.Y.) 122:373 (1979).
T. M. Liggett,Interacting Particle Systems (Springer, New York, 1985).
T. E. Harris, Contact iterations on a lattice,Ann. Prob. 2:969 (1974).
C. Kipnis and C. Newman, The metastable behavior of infrequently observed, weakly random, one-dimensional diffusion processes,SIAM J. Appl. Math. (to appear).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Schonmann, R.H. Metastability for the contact process. J Stat Phys 41, 445–464 (1985). https://doi.org/10.1007/BF01009017
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01009017