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Extended Systems with Deterministic Local Dynamics and Random Jumps

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Abstract

We consider particle systems on lattices with internal dynamics at each site and random jumps between sites. Models with simple chaotic local dynamics, namely expanding circle maps, are considered. Results on mean drift rates, central limit theorems and dependences on jump parameters are proved.

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References

  1. Conze J.-P. (1999). Sur un critere de recurrence en dimension 2 pour les marches stationnaires, applications. Ergodic Theory Dynam. Sys. 19(5): 12331245

    Google Scholar 

  2. Dunford, N., Schwartz, J.: Linear Operators, Part I. New York: Wiley, 1957 (Sect. VII.6 in particular)

  3. Eckmann J.-P. and Young L.-S. (2006). Nonequilibrium energy profiles for a class of 1-D models. Commun. Math. Phys. 262: 237–267

    Article  MATH  ADS  Google Scholar 

  4. Grosfils P., Boon J.P., Cohen E.G.D. and Bunimovich L. (1999). Propagation and Organization in Random Media. J. Stat. Phys. 97: 575–608

    Article  MATH  Google Scholar 

  5. Hennion H. (1993). Sur un theoreme spectral et son application aux noyaux Lipchitziens. Proc. Am. Math. Soc. 118: 627–634

    Article  MATH  Google Scholar 

  6. Kobre, E.: Rates of diffusion in dynamical systems with random jumps. Ph.D. thesis, New York University (2005)

  7. Lasota A. and Yorke J.A. (1973). On the existence of invariant measures for piecewise monotonic transformations. Trans. Amer. Math. Soc. 186: 481–488

    Article  Google Scholar 

  8. Larralde H., Leyvraz F. and Mejia-Monasterio C. (2003). Transport properties of a modified Lorentz gas. J. Stat. Phys. 113: 197–231

    Article  MATH  Google Scholar 

  9. Liverani, C.: Central limit theorem for deterministic systems. In: International Conference on Dynamical Systems (Montevideo 1995), Pitman Research Notes in Math. Series 362, London: CRC Press, 1997

  10. Neveu J. (1965). Mathematical foundations of the calculus of probability. Holden-Day, San Francisco, CA

    MATH  Google Scholar 

  11. Schmidt K. (1998). On joint recurrence. Comptes Rendu Acad. Sci. Paris Ser. I Math. 327(9): 837–842

    Article  MATH  Google Scholar 

  12. Sinai Ya.G. (1970). Dynamical systems with elastic relections: Ergodic properties of dispersing billiards. Russ. Math. Surv. 25(2): 137–189

    Article  Google Scholar 

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Authors and Affiliations

  1. New York, NY, USA

    Elisha Kobre

  2. Courant Institute of Mathematical Sciences, 251 Mercer St., New York, NY, 10012, USA

    Lai-Sang Young

Authors
  1. Elisha Kobre
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  2. Lai-Sang Young
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Correspondence to Lai-Sang Young.

Additional information

Communicated by A. Kupiainen

A version of most of the results in this paper is contained in this author’s Ph.D. thesis [K].

This research is partially supported by a grant from the NSF.

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Kobre, E., Young, LS. Extended Systems with Deterministic Local Dynamics and Random Jumps. Commun. Math. Phys. 275, 709–720 (2007). https://doi.org/10.1007/s00220-007-0312-5

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  • DOI: https://doi.org/10.1007/s00220-007-0312-5

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