Skip to main content
SpringerLink
Log in

Transformation of recursion relations for generalized random walks

  • Published:
Zeitschrift für Physik B Condensed Matter

Abstract

It is shown that recursion relation for the generalized random walks (GRW) or correlated random walks can be directly transformed into the recursion relation for the usual random walks. The recursion relation for the GRW is expressed by a non-linear difference equation. To transform the non-linear difference equation, the Hopf-Cole transformation is modified and expressed in a discrete form. Formal solution of the GRW is obtained in an integral representation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Haken, H.: Introduction to Synergetics: Nonequilibrium Phase Transitions and Self organization in Physics, Chemistry and Biology, Berlin, Heidelberg, New York: Springer 1977 See also

    Google Scholar 

  2. Weidlich, W.: Collective Phenomena1, 51 (1972)

    Google Scholar 

  3. Nicolis, G., Prigogine, I.: Self-Organization in Nonequilibrium System-From Dissipative Structures to Order through Fluctuation. New York: John Wily 1977

    Google Scholar 

  4. May, R.M.: Science186, 645 (1974)

    Google Scholar 

  5. Nakamura, K.: Prog. Theor. Phys. Suppl.64, 378 (1978)

    Google Scholar 

  6. Ebeling, W., Schimansky, L.: Physica98A, 589 (1979)

    Google Scholar 

  7. Schlögl, F.: Z. Physik253, 147 (1972)

    Google Scholar 

  8. Huber, D.L.: Phys. Rev.B15, 533 (1977)

    Google Scholar 

  9. Richard, P.M.: Phys. Rev.B16, 1399 (1977)

    Google Scholar 

  10. Hara, H.: Read at the 39th Statistical Mechanics Meeting. Rutgers Univ., May 1978

  11. Hara, H.: Phys. Rev.B20, 4062 (1979)

    Google Scholar 

  12. Hara, H., Choi, S.D.: Z. Physik B38, 351 (1980)

    Google Scholar 

  13. Hara, H.: Z. Physik B36, 369 (1980)

    Google Scholar 

  14. Uhlenbeck, G.E., Ornstein, L.S.: Phys. Rev.36, 823 (1930)

    Google Scholar 

  15. Chandrasekhar, S.: Rev. Mod. Phys.15, 1 (1943) See also

    Google Scholar 

  16. Montroll, E.W., Weiss, G.E.: J. Math. Phys.6, 167 (1965)

    Google Scholar 

  17. Burgers, J.M.: Proc. Acad. Sco. Amsterdam53, 247 (1950)

    Google Scholar 

  18. Burgers, J.M.: Statistical models and turbulence. 41 Rosenblatt, M., Van Atta, C. (eds.), Vol. 41, Berlin, Heidelberg, New York: Springer 1972

    Google Scholar 

  19. Hopf, E.: Commun. Pure Appl. Math.3, 201 (1950)

    Google Scholar 

  20. Cole, J.D.: Q. Appl. Math.9, 225 (1951)

    Google Scholar 

  21. Yamaguchi, M.: Non-linear Phenomena and Its analysis. Yamaguchi, M. (ed.). Tokyo: Nippon Hyoronsha 1979

    Google Scholar 

  22. Yamaguchi, M., Matano, H.: Proc. Jpn. Acad. Ser. A55, 78 (1979)

    Google Scholar 

  23. Tatsumi, T., Kida, S.: J. Fluid Mech.55, 659 (1972)

    Google Scholar 

  24. Jeng, D.T., Foerster, R., Haaland, S., Meecham, W.C.: Phys. Fluids9, 2114 (1966)

    Google Scholar 

  25. Hosokawa, I., Yamamoto, K.: J. Stat. Phys.13, 245 (1975)

    Google Scholar 

  26. Cukier, R.I., Lakatos-Lindenberg, K., Shuler, K.E.: J. Stat. Phys.9, 137 (1973)

    Google Scholar 

  27. Weiss, G.H.: J. Stat. Phys.21, 609 (1979)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Science, Faculty of Engineering, 980, Sendai, Tohoku University, Japan

    Hiroaki Hara

Authors
  1. Hiroaki Hara
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hara, H. Transformation of recursion relations for generalized random walks. Z. Physik B - Condensed Matter 39, 261–267 (1980). https://doi.org/10.1007/BF01292671

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01292671

Keywords

Search

Navigation