Abstract
We show the existence of a constant γ∈(0, ∞) such that if τ n is the extinction time for a supercritical contact process on [1, n]d starting from full occupancy, then {log(E[τ n])}/n d tend to γ as n tends to infinity.
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REFERENCES
J. W. Chen, The contact process on a finite set in higher dimensions, Chinese J. Contemp. Math. 15:13-20 (1994).
R. Durrett, Lecture Notes on Particle Systems and Percolation (Wadsworth, Pacific Grove, 1988).
R. Durrett, Oriented percolation in two dimensions, Ann. Prob. 12:999-1040 (1984).
R. Durrett and X.-F. R. Liu, The contact process on a finite set, Ann. Prob. 16:1158-1173 (1988).
C. Bezuidenhout and G. Grimmett, The critical contact process dies out, Ann. Prob. 18:1462-1482 (1990).
R. Durrett and R. Schonmann, The contact process on a finite set II, Ann. Prob. 16:1570-1584 (1988).
T. M. Liggett, Interacting Particle Systems (Springer, Berlin, New York, 1985).
T. Mountford, A metastable result for the finite multidimensional contact process, Canadian Mathematical Bulletin 36:216-226 (1993).
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Mountford, T.S. Existence of a Constant for Finite System Extinction. Journal of Statistical Physics 96, 1331–1341 (1999). https://doi.org/10.1023/A:1004652719999
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DOI: https://doi.org/10.1023/A:1004652719999