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Dualities for a Class of Finite Range Probabilistic Cellular Automata in One Dimension

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Abstract

In this paper we study dualities for a class of one-dimensional probabilistic cellular automata with finite range interactions by using a sequence of extended cellular automata.

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REFERENCES

  1. M. Katori, N. Konno, A. Sudbury, and H. Tanemura, Dulalities for the Domany-Kinzel model, preprint (2001).

  2. E. Domany and W. Kinzel, Equivalence of cellular automata to Ising models and directed percolation, Phys. Rev. Lett. 53:31–314 (1984).

    Google Scholar 

  3. W. Kinzel, Phase transitions of cellular automata, Z. Phys. B58:22–244 (1995).

    Google Scholar 

  4. S. Wolfram, Statistical mechanics of cellular automata, Rev. Modern Phys. 55:60–644 (1983).

    Google Scholar 

  5. S. Wolfram, Universality and complexity in cellular automata, Physica D 10:–35 (1984).

    Google Scholar 

  6. R. Durrett, Lecture Notes on Particle Systems and Percolation (Wadsworth, Inc., California, 1988).

    Google Scholar 

  7. A. W. Sudbury and P. Lloyd, Quantum operators in classical quantum theory. II. The concept of duality in interacting particle systems, Ann. Probab. 23:181–1830 (1995).

    Google Scholar 

  8. A. W. Sudbury and P. Lloyd, Quantum operators in classical quantum theory. IV. Quasiduality and thinnings of interacting particle systems, Ann. Probab. 25:9–114 (1997).

    Google Scholar 

  9. C. Bandt, The geometry of a parameter space of interacting particle systems, J. Stat. Phys. 96:88–906 (1999).

    Google Scholar 

  10. A. W. Sudbury, Dual families of interacting particle systems on graphs, J. Theoret. Probab. 13:69–716 (2000).

    Google Scholar 

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Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Engineering, Yokohama National University, Hodogaya-ku, Yokohama, 240-8501, Japan

    Norio Konno

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  1. Norio Konno
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Konno, N. Dualities for a Class of Finite Range Probabilistic Cellular Automata in One Dimension. Journal of Statistical Physics 106, 915–922 (2002). https://doi.org/10.1023/A:1014025501317

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  • DOI: https://doi.org/10.1023/A:1014025501317

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