Skip to main content
SpringerLink
Log in

Random walk on a disordered directed Bethe lattice

  • Articles
  • Published:
Journal of Statistical Physics Aims and scope Submit manuscript

Abstract

The random walk of a particle on a directed Bethe lattice of constant coordinanceZ is examined in the case of random hopping rates. As a result, the higher the coordinance, the narrower the regions of anomalous drift and diffusion. The annealed and quenched mean square dispersions are calculated in all dynamical phases. In opposition to the one-dimensional (Z=2) case, the annealed and quenched mean quadratic dispersions are shown to be identical in all phases.

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. J. P. Bouchaud and A. Georges,Phys. Rep. 195:127 (1990).

    Google Scholar 

  2. C. Aslangul, M. Barthélémy, N. Pottier, and D. Saint-James,J. Stat. Phys. 59:11 (1990).

    Google Scholar 

  3. C. Aslangul, M. Barthélémy, N. Pottier, and D. Saint-James,J. Stat. Phys. 61:399 (1990).

    Google Scholar 

  4. F. Peruggi,J. Math. Phys. 25:3303 (1984).

    Google Scholar 

  5. F. Peruggi,J. Math. Phys. 25:3316 (1984).

    Google Scholar 

  6. J. W. Essam and M. E. Fisher,Rev. Mod. Phys. 42:272 (1970).

    Google Scholar 

  7. P. Le Doussal and J. Machta,Phys. Rev. B 40:9427 (1989).

    Google Scholar 

  8. B. D. Hughes and M. Sahimi,J. Stat. Phys. 29:781 (1982).

    Google Scholar 

  9. C. Aslangul, M. Barthélémy, N. Pottier, and D. Saint-James,J. Stat. Phys., to be published.

  10. B. Derrida and H. Spohn,J. Stat. Phys. 51:817 (1988).

    Google Scholar 

  11. B. Derrida,Physica 163A:71 (1990).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Groupe de Physique des Solides, Laboratoire associé au CNRS (UA n∘ 17) et aux Universités Paris VII et Paris VI, Tour 23, 2 place Jussieu, 75251, Paris Cedex 05, France

    C. Aslangul, M. Barthélémy & N. Pottier

  2. Laboratoire de Physique Statistique, Collège de France, 3 rue d'Ulm, 75231, Paris Cedex 05, France

    D. Saint-James

  3. Université Paris VII, France

    D. Saint-James

Authors
  1. C. Aslangul
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Barthélémy
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. N. Pottier
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. D. Saint-James
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

We shall employ indifferently the expressions Bethe lattice or infinite Cayley tree to denote an infinite ramified lattice of constant coordinanceZ.(4, 5)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Aslangul, C., Barthélémy, M., Pottier, N. et al. Random walk on a disordered directed Bethe lattice. J Stat Phys 65, 695–713 (1991). https://doi.org/10.1007/BF01053749

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01053749

Keywords

Search

Navigation