Abstract
We consider survival probabilities for the discrete-time process in one dimension, which is known as the Domany–Kinzel model. A convergence theorem for infinite systems can be obtained in the nonattractive case.
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REFERENCES
R. Durrett, Lecture Notes on Particle Systems and Percolation (Wadsworth, California, 1988).
E. Domany and W. Kinzel, Equivalence of cellular automata to Ising models and directed percolation, Phys. Rev. Lett. 53:311–314 (1984).
D. Griffeath, Limit theorems for nonergodic set-valued Markov processes, Ann. Probab. 6:379–387 (1978).
N. Inui, N. Konno, G. Komatsu and K. Kameoka, Local directed percolation probability in two dimensions, J. Phys. Soc. Jpn. 67:99–102 (1998).
A. Sudbury and P. Lloyd, Quantum operators in classical probability theory: II. The concept of duality in interacting particle systems, Ann. Probab. 23:1816–1830 (1995).
A. Sudbury and P. Lloyd, Quantum operators in classical probability theory: IV. Quasi-duality and thinnings of interacting particle systems, Ann. Probab. 25:96–114 (1997).
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Katori, M., Konno, N. & Tanemura, H. Survival Probabilities for Discrete-Time Models in One Dimension. Journal of Statistical Physics 99, 603–612 (2000). https://doi.org/10.1023/A:1018617328216
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DOI: https://doi.org/10.1023/A:1018617328216