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Large Deviations and Ergodicity for Spin Particle Systems

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Abstract

In this paper we investigate the large deviation principle (LDP) for spin particle systems with possibly vanishing flip rates. The situation turns out to be much more complicated if the flip rates are allowed to be zero than the one considered by Dai, where the systems are assumed to have strictly positive flip rates. The upper and lower large-deviation bounds are studied, respectively. The two governing rate functions are compared and a variational principle is given. We then apply the results to obtain some new large-deviation estimates for the occupation times of attractive systems. In particular, we prove a strong form of exponential convergence for ergodic systems.

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REFERENCES

  1. M. Bramson, J. T. Cox, and D. Griffeath, Occupation time large deviations of the voter model, Probab. Th. Rel. Fields 77:401–413 (1988).

    Google Scholar 

  2. C. Bezuidenhout and G. Grimmett, The critical contact processes dies out. Ann. Prob. 18:1462–1482 (1990).

    Google Scholar 

  3. J. T. Cox and D. Griffeath, Large deviations for some infinite particle system occupation times, Contemp. Math. 41:43–54 (1985).

    Google Scholar 

  4. P. Dai Pra, Space-time large deviations for interacting particle systems, Comm. Pure Appl. Math. 387–422 (1993).

  5. P. Dai Pra, Large deviations and stationary measures for interacting particle systems, Stoch. Processes Appl. 48:9–30 (1993).

    Google Scholar 

  6. J. D. Deuschel and D. W. Stroock, Large Deviation (Academic Press, New York, 1989).

    Google Scholar 

  7. H. Föllmer, Random Fields and Diffusion Processes. École d'Été de Probabilités de saintflour XV–XV2, Lecture Notices in Math., Vol. 1362, pp. 101–203, Springer-Verlag (1988).

  8. D. Griffeath, The basic contact processes, Stoch. Processes Appl. 151–186 (1981).

  9. C. Landim, Occupation time large deviations for the symmetric simple exclusion process, Ann. Probab. 20:206–231 (1992).

    Google Scholar 

  10. J. L. Lebowitz and R. H. Schonmann, Pseudo-free energies and large deviations for non Gibbsian FKG measures, Probab. Th. Rel. Rields 77:49–64 (1988).

    Google Scholar 

  11. T. M. Liggett, Interacting Particle Systems (Springer-Verlag, New York, 1985).

    Google Scholar 

  12. S. R. S. Varadlian, Large deviations and Applications. CBMS-NSF Regional Conference Series in Applied Mathematics, Vol. 46, Philadelphia, SIAM (1984).

    Google Scholar 

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Authors and Affiliations

  1. Department of Applied Mathematics, Tsinghua University, Beijing, 100084, China

    Jinwen Chen

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  1. Jinwen Chen
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Chen, J. Large Deviations and Ergodicity for Spin Particle Systems. Journal of Statistical Physics 91, 369–393 (1998). https://doi.org/10.1023/A:1023056524668

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  • DOI: https://doi.org/10.1023/A:1023056524668

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