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Random walks with memory

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La Rivista del Nuovo Cimento (1978-1999) Aims and scope

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References

  1. L. Pietronero andE. Tosatti:Fractals in Physios (North-Holland, Amsterdam, New York, N. Y., 1986).

    Google Scholar 

  2. P. G. de Gennes:Scaling Concepts in Polymer Physics (Cornell University Press, Ithaca, N. Y., 1979).

    Google Scholar 

  3. P. J. Flory:Principles of Polymer Chemistry (Cornell University Press, Ithaca, N. Y., 1953).

    Google Scholar 

  4. L. Pietronero:Phys. Rev. B,27, 5887 (1983).

    Article  ADS  Google Scholar 

  5. D. J. Amit:Field Theory, the Renormalization Group and Critical Phenomena (McGraw-Hill Int., New York, N. Y., 1978).

    Google Scholar 

  6. F. Spitzer:Principles of Random Walk (Springer-Verlag, New York, N. Y., 1976).

    Book  MATH  Google Scholar 

  7. G. H. Weiss andE. J. Rubin:Adv. Chem. Phys.,62, 363 (1983). For the random walk in disordered media that we do not discuss here seeS. Alexander, J. Bernasconi, W. R. Schneider and R. Orback:Rev. Mod. Phys.,53, 175 (1981);M. F. Shlesinger and E. W. Montroll:Proc. Natl. Acad. Sci. USA,81, 1280 (1984).

    Google Scholar 

  8. B. B. Mandelbrot:The Fractal Geometry of Nature (W. H. Freeman, New York, N. Y., 1983).

    Google Scholar 

  9. W. R. Schneider: inTrends and Developments in the 80’s, Bielefeld Math-Phys. 4 and 5, edited byS. Albeverio andP. Blancherd (World Scientific Publ. Co., Singapore, 1985), p. 349.

    Google Scholar 

  10. W. Feller:An Introduction to Probability Theory and its Applications, Vol. 1 and 2 (Wiley, New York, N. Y., 1971).

    MATH  Google Scholar 

  11. M. L. Huggins:J. Phys. Chem.,46, 151 (1942). See also the discussion in Chapt. III of ref. [2].

    Article  Google Scholar 

  12. I. Majid, Z. V. Djordjevic andH. E. Stanley:Phys. Rev. Lett.,51, 1282 (1983).

    Article  MathSciNet  ADS  Google Scholar 

  13. B. Nienhuis:Phys. Rev. Lett.,49, 1062 (1982).

    Article  MathSciNet  ADS  Google Scholar 

  14. S. P. Obukhov:J. Phys. A,17, L965 (1984).

    Article  ADS  Google Scholar 

  15. R. Vilanove andF. Rondelez:Phys. Rev. Lett.,45, 1502 (1980);A. Takahashi, A. Yoshida and M. Kawaguchi:Macromolecules,15, 1196 (1982);A. Baumgabtneb:J. Phys. (Paris),43, 1407 (1982);A. L. Kholodenko and K. F. Freed:J. Phys. A,17, L191 (1984);M. J. Stephen:Phys. Lett. A,53, 363 (1975).

    Article  ADS  Google Scholar 

  16. P. G. de Gennes:Phys. Lett. A,38, 339 (1972).

    Article  ADS  Google Scholar 

  17. L. Peliti: inFractals in Physics (North-Holland, Amsterdam, New York, N. Y., 1986), p. 73;L. Pietronero and L. Peliti: inFractals in Physics (North-Holland, Amsterdam, New York, N. Y., 1986), p. 83.

    Google Scholar 

  18. L. Pietronero:Phys. Rev. Lett.,55, 2025 (1985).

    Article  ADS  Google Scholar 

  19. L. Pietronero andL. Peliti:Phys. Rev. Lett.,55, 1479 (1985).

    Article  ADS  Google Scholar 

  20. L. Peliti:J. Phys. (Paris) Lett.,45, L925 (1984).

    Article  Google Scholar 

  21. P.C. Martin, E. D. Siggia andH.A. Rose:Phys. Rev. A,7, 423 (1973).

    Article  ADS  Google Scholar 

  22. L. Peliti:J. Phys. (Paris),46, 1469 (1985).

    Article  Google Scholar 

  23. M. Doi:J. Phys. A,9, 1465, 1479 (1976).

    Article  ADS  Google Scholar 

  24. P. Gbassbebger andM. Scheunert:Fortschr. Phys.,28, 547 (1980).

    Article  MathSciNet  Google Scholar 

  25. D. J. Amit, G. Parisi andL. Peliti:Phys. Rev. B,27, 1635 (1983).

    Article  MathSciNet  ADS  Google Scholar 

  26. F. J. Wegner:Phys. Rev. B,5, 4529 (1972);6, 1891 (1972).

    Article  ADS  Google Scholar 

  27. J. Beenasconi andL. Pietronero:Phys. Rev. B,29, 5196 (1984);S. L. A. de QueiRoz, A. L. Stella and R. B. Stinchcombe:J. Phys. A,17, L45 (1984), and to be published;H. C. Ottinger:J. Phys. A,18, 363 (1985).

    Article  ADS  Google Scholar 

  28. E. Kammal, J. C. Anglès D’Auriac andA. Benoit:J. Phys. A,17, L9 (1984).

    Article  Google Scholar 

  29. S. P. Obukhov:J. Phys. A,17, L7 (1984).

    Article  ADS  Google Scholar 

  30. S. P. Obukhov andL. Peliti:J. Phys. A,16, L147 (1983).

    Article  MathSciNet  ADS  Google Scholar 

  31. L. Peliti:Phys. Rep.,103, 225 (1984).

    Article  MathSciNet  ADS  Google Scholar 

  32. G. E. Uhlenbeck andL. S. Ornstein:Phys. Rev.,36, 823 (1930).

    Article  ADS  MATH  Google Scholar 

  33. C. Byrnes andA. J. Guttmann:J. Phys. A,17, 3335 (1984).

    Article  MathSciNet  ADS  Google Scholar 

  34. E. C. Dekeyser: unpublished.

  35. J. Adler: private communication.

  36. J. W. Lyklema andK. Kremer:J. Phys. A,17, L691 (1984).

    Article  ADS  Google Scholar 

  37. I. Majid, N. Jan, A. Coniglio andH. E. Stanley:Phys. Rev. Lett.,52, 1257 (1984).

    Article  ADS  Google Scholar 

  38. L. Peliti:J. Phys. (Paris) Lett.,45, L925 (1984).

    Article  Google Scholar 

  39. K. Kremer andJ. W. Lyklema:Phys. Rev. Lett.,55, 2091(C) (1985);J. W. Lyklema and K. Kremer:J. Phys. A,19, 275 (1986).

    Article  ADS  Google Scholar 

  40. I. Majid, N. Jan, A. Coniglio and H. E. Stanley: preprint.

  41. A. Coniglio and N. Jan: private communication.

  42. K. Kremer andJ. W. Lyklema:Phys. Rev. Lett.,54, 267 (1985).

    Article  ADS  Google Scholar 

  43. A. Weinrib andS.A. Trugman:Phys. Rev. B,31, 2993 (1985).

    Article  ADS  Google Scholar 

  44. J. W. Lyklema:J. Phys. A,18, L617 (1985).

    Article  ADS  Google Scholar 

  45. K. Ziff:Phys. Rev. Lett.,56, 545 (1986).

    Article  ADS  Google Scholar 

  46. J. W. Lyklema, C. Evertsz andL. Pietronero:Europhys. Lett.,2, 77 (1986);J. W. Lyklema and C. Evertsz: inFractals in Physics (North-Holland, Amsterdam, New York, N. Y., 1986), p. 87.

    Article  ADS  Google Scholar 

  47. L. Niemeyer, L. PIetronero andH. J. Wiesmann:Phys. Rev. Lett.,52, 1033 (1984);L. Pietronero and H. J. Wiesmann:J. Stat. Phys.,36, 881 (1984).

    Article  MathSciNet  ADS  Google Scholar 

  48. J. W. Lyklema and C. Evertsz: to be published.

  49. T. A. Witten andL. M. Sander:Phys. Rev. Lett.,47, 1400 (1981).

    Article  ADS  Google Scholar 

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Peliti, L., Pietronero, L. Random walks with memory. Riv. Nuovo Cim. 10, 1–33 (1987). https://doi.org/10.1007/BF02742985

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