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Algorithmical Unsolvability of the Ergodicity Problem for Locally Interacting Processes with Continuous Time

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Abstract

We prove algorithmical unsolvability of the ergodicity problem for a class of one-dimensional translation-invariant random processes with local interaction with continuous time, also known as interacting particle systems. The set of states of every component is finite, the interaction occurs only between nearest neighbors, only one particle can change its state at a time and all rates are 0 or 1.

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REFERENCES

  1. Thomas M. Liggett, Interacting Particle Systems (Springer, 1985).

  2. G. Kurdyumov, An algorithm-theoretic method in studying homogeneous random networks, in Locally Interacting Systems and Their Application in Biology, R. Dobrushin, V. Kryukov, and A. Toom, eds., Lecture Notes in Mathematics, Vol. 653 (Springer, 1978), pp. 37–55.

  3. G. Kurdyumov, An algorithm-theoretic method for the study of homogeneous random networks, Adv. Probab. 6:471–504 (1980).

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  4. A. Toom, N. Vasilyev, O. Stavskaya, L. Mityushin, G. Kurdyumov, and S. Pirogov, Discrete Local Markovj Systems, in Stochastic Cellular Systems: Ergodicity, Memory, Morphogenesis, R. Dobrushin, V. Kryukov, and A. Toom, eds., Nonlinear Science: Theory and Applications (Manchester University Press, 1990), pp. 1–182.

  5. P. Berman and J. Simon, Investigations of Fault-Tolerant Networks of Computers (preliminary version), Proc. of the 20th Annual ACM Symp. on the Theory of Computing (1988), pp. 66–77.

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Authors and Affiliations

  1. Department of Statistics, Federal University of Pernambuco, Recife, PE, 50740-540, Brazil

    André Toom

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  1. André Toom
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Toom, A. Algorithmical Unsolvability of the Ergodicity Problem for Locally Interacting Processes with Continuous Time. Journal of Statistical Physics 98, 495–501 (2000). https://doi.org/10.1023/A:1018699527637

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  • DOI: https://doi.org/10.1023/A:1018699527637

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