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Multidimensional RWRE with Subclassical Limiting Behavior

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Random Media

Part of the book series: The IMA Volumes in Mathematics and Its Applications ((IMA,volume 7))

Abstract

This paper is based on a talk given at the workshop on Random Media, September 17–24 at the IMA, and like the talk it describes two results proved in [4] and [5].

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References

  1. B, Derrida and J.M. Luck (1983), Diffusion on a random lattice: weak disorder expansion in orbitrary dimension, Phys. Rev. B, 28, 7183–7190.

    Article  Google Scholar 

  2. R. Durrett (1985a), Reversible Diffusion Processes to appear in Probability and Harmonic Analysis, edited by J. Chao, and W. Woyczynski, Publ. by Marcel Dekker, New York.

    Google Scholar 

  3. R. Durrett (1985b), Particle systems, random media, and large deviations. Conference proceedings, AMS Contemporary Math Series, vol. 41.

    Google Scholar 

  4. R. Durrett (1986a), Some multidmensional RWRE with subclassical limiting behavior. Comm. Math. Phys., 104, 87–102.

    Article  MathSciNet  MATH  Google Scholar 

  5. R. Durrett (1986b), Two comparison theorems for the recurrence of Markov chains. Am. Prob. submitted for publication.

    Google Scholar 

  6. R. Figari, E. Orlandi, G. Papanicolaou (1983), Diffusive behavior of a random walk in random media, Taniguichi Symp. Katata, publ. by Kodansha, Japan

    Google Scholar 

  7. D. Fisher (1984), Random walks in random environments, Bell Laboratories, preprint.

    Google Scholar 

  8. R. Gangoli (1965), Abstract harmonic Analysis and Levy’s Brownian motion of several parameters, 5th Berkeley Symp. Vol. II, 13–30.

    Google Scholar 

  9. D. Griffeath, T. Liggett (1982), Critical phenomena for Spitzer’s reversible nearest particle systems, Ann. Prob. 10, 881–895.

    Article  MathSciNet  MATH  Google Scholar 

  10. S. Kalikow (1981), Generalized random walk in a random environment. Ann. Prob. 9, 753–768.

    Article  MathSciNet  Google Scholar 

  11. E. S. Key (1984), Recurrence and transience criteria for random walk in a random environment, Ann. Prob. 12, 529–560.

    Article  MathSciNet  MATH  Google Scholar 

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

    MATH  Google Scholar 

  13. E. Marinari, G. Parisi, D. Ruelle, P. Windey (1983a), Random walks in a random envi ronment and 1/f noise, Phys. Rev. Letters 50, 1223–1225.

    Article  MathSciNet  Google Scholar 

  14. E. Marinari, G. Parisi, D. Ruelle, P. Windey (1983b), On the interpretation of 1/f noise, Comm. Math. Phys., 89, 1–12.

    Article  MathSciNet  MATH  Google Scholar 

  15. H. Osada (1983), Homogenization of diffusion processes with random coefficients, p. 507–517 in Proceedings of the 4th Japan USSR Probability Symposium, Springer LNM 1021.

    Google Scholar 

  16. G. C. Papanicolaou (1983), Diffusions and random walks in random media in The Mathematics and Physics of Disordered Media ed. by B.D. Hughes and B.W. Ninham, Springer LNM 1035.

    Google Scholar 

  17. G. Papanicolaou and O. Pironeau (1981), On the asymptotic behavior of motions in random flows, p. 36–41 in Stochastic Nonlinear Systems in Phsyics, Chemistry, and Biology, edited by L. Arnold and R. Lefever, Springer-Verlag.

    Google Scholar 

  18. G. Papanicolaou, S. R. S. Varadhan (1979), Boundary value problems with rapidly oscillating coefficients, p. 835–873 in Random Fields edited by J. Lebowitz and D. Szaxa, North Holland.

    Google Scholar 

  19. G. Papanicolaou, S. R. S. Varadhan (1981), Diffusions with random coefficients, p. 253–262 in Essays in Statistics and Probability edited by G. Kallianpur, P. Krishnaiah, and J. Ghosh, North Holland.

    Google Scholar 

  20. L. D. Pitt (1978), Local times for Gaussian vector fields, Indiana Math. J. 27, 309–330.

    Article  MathSciNet  MATH  Google Scholar 

  21. S. Schumacher (1984), Diffusions with random coefficients, Ph.D. Thesis, UCLA, A summary appears in Durrett (1985b).

    Google Scholar 

  22. Ya. Sinai (1982), Limit behavior of one-dimensional random walks in random environments, Theor. Probab. Appl. 27, 247–258.

    MathSciNet  Google Scholar 

  23. F. Solomon (1975), Random walks in a random environment, Ann. Prob. 3, 1–31.

    Article  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, Cornell University, White Hall Ithaca, New York, 14853-7901, USA

    Richard Durrett

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  1. Richard Durrett
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Editor information

Editors and Affiliations

  1. Institute for Mathematics and Its Applications, Minneapolis, Minnesota, 55455, USA

    George Papanicolaou

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© 1987 Springer-Verlag New York, Inc.

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Durrett, R. (1987). Multidimensional RWRE with Subclassical Limiting Behavior. In: Papanicolaou, G. (eds) Random Media. The IMA Volumes in Mathematics and Its Applications, vol 7. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8725-1_7

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  • DOI: https://doi.org/10.1007/978-1-4613-8725-1_7

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4613-8727-5

  • Online ISBN: 978-1-4613-8725-1

  • eBook Packages: Springer Book Archive

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