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Stochastic bounds on the zero range processes with superlinear jump rates

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Abstract

We present some results concerning the regularity of dynamics of the zero-range process. These results are achieved by using coupling based on attractivity of the models. The essential novelty is that these methods are carried out without any restriction on the increase of the jump rates depending on the local configurations, in contrast to the usually required sub-linear growth conditions. Based on the bounds presented here, the dynamics of these models may be constructed.

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References

  1. E. D. Andjel, Invariant measures for the zero range process, The Annals of Prob. 10(3) (1982), 325–547.

    MathSciNet  Google Scholar 

  2. M. Balázs, Microscopic shape of shocks in a domain growth model, Journal of Stat.Phys. 105 (3/4) (2001), 511–524.

    Article  MATH  Google Scholar 

  3. M. Balázs, Growth fluctuations in a class of deposition models, Annales de l'Institut Henri Poincaré, Vol. 39, Issue 4, 2003, 639–685.

    Article  MATH  Google Scholar 

  4. L. Booth, Random Spatial Structures and Sums, PhD thesis, Utrecht University, 2002.

  5. T. M. Liggett, An infinite particle system with zero range interactions, The Annals of Prob. 1 (2) (1973), 240–253.

    MATH  MathSciNet  Google Scholar 

  6. T. M. Liggett, Interacting particle systems, Springer-Verlag, 1985.

  7. C. Quant, On the construction and stationary distributions of some spatial queueing and particle systems, PhD thesis, Utrecht University, 2002.

  8. F. Rezakhanlou, Microscopic structure of shocks in one conservation laws, Ann Inst.H.Poincaré Anal.Non Linéaire 12 (2) (1995), 119–153.

    MATH  MathSciNet  Google Scholar 

  9. S. Sethuraman, On extremal measures for conservative particle systems, Ann.Inst.H.Poincaré 37(2) (2001), 139–154.

    Article  MATH  MathSciNet  Google Scholar 

  10. F. Spitzer, Interaction of markov processes, Adv.in Math. 5 (1970), 246–290.

    Article  MATH  MathSciNet  Google Scholar 

  11. H. Thorisson, Coupling, Stationarity, and Regeneration, Springer, 2000.

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Authors and Affiliations

  1. Institute of Mathematics, Technical University Budapest, H-1111, Budapest, Egry József u. 1 H ép. V, Hungar

    Márton Balázs

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  1. Márton Balázs
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Balázs, M. Stochastic bounds on the zero range processes with superlinear jump rates. Periodica Mathematica Hungarica 47, 17–27 (2003). https://doi.org/10.1023/B:MAHU.0000010808.13199.d9

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  • DOI: https://doi.org/10.1023/B:MAHU.0000010808.13199.d9

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