Abstract
The right edge of a nearest neighbor supercritical contact process satisfies a central limit theorem.(8, 9) In this paper, a block construction is created to extend the argument by Kuczek(9) to the nonnearest neighbor case. The proof of the following fact in the nonnearest neighbor case is the key to the extension: There is a positive chance that the rightmost particle at time 0 infects the rightmost particle at every time.
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REFERENCES
Bezuidenhout, C., and Grimmett, G. (1990). The critical contact process dies out. Ann. Prob. 18, 1462–1486.
Bezuidenhout, C., and Gray, L. (1994). Critical attractive spin systems. Ann. Prob. 22, 1160–1194.
Durrett, R. (1980). On the growth of one-dimensional contact processes. Ann. Prob. 8, 890–907.
Durrett, R. (1984). Oriented percolation in two dimensions. Ann. Prob. 12, 999–1040.
Durrett, R. (1988). Lecture Notes on Particle Systems and Percolation, Wadsworth.
Durrett, R. (1995). Ten lectures on particle systems. St. Flour Summer School, Vol. 1608, SLNM.
Durrett, R. (1996). Probability: Theory and Examples, Duxbury Press.
Galves, A., and Presutti, E. (1987). Edge fluctuations for the one-dimensional supercritical contact process. Ann. Prob. 15, 1131–1145.
Kuczek, T. (1989). The central limit theorem for the right edge of supercritical oriented percolation. Ann. Prob. 17, 1322–1332.
Liggett, T. (1985). Interacting Particle Systems, Springer-Verlag.
Sweet, T. (1997). One dimensional spin systems, Ph.D. thesis, University of California, Los Angeles.
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Mountford, T.S., Sweet, T.D. An Extension of Kuczek's Argument to Nonnearest Neighbor Contact Processes. Journal of Theoretical Probability 13, 1061–1081 (2000). https://doi.org/10.1023/A:1007818108889
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DOI: https://doi.org/10.1023/A:1007818108889