Skip to main content

Advertisement

SpringerLink
Log in
Menu
Find a journal Publish with us
Search
Cart
  1. Home
  2. Probability Theory and Related Fields
  3. Article
Spectra of graphs and fractal dimensions. I
Download PDF
Download PDF
  • Published: December 1990

Spectra of graphs and fractal dimensions. I

  • András Telcs1 

Probability Theory and Related Fields volume 85, pages 489–497 (1990)Cite this article

  • 153 Accesses

  • 14 Citations

  • Metrics details

Summary

In this paper we consider the nearest neighbour Random Walk on infinite graphs. We discuss the connection between the two smallest eigenvalues of the Laplacian of the graph and the diffusion speed of the RW.

Download to read the full article text

Working on a manuscript?

Avoid the common mistakes

References

  • [A] Alon, N.: Eigenvalues and expanders. combinatorica6, 83–89 (1986)

    Google Scholar 

  • [AM] Alon, N, Milman, V.D.: λ1 Isoperimetric inequalities for graphs and superconcentrators. J. of Comb. Theory, Ser. B38, 73–88 (1985)

    Google Scholar 

  • [C] Cheeger, J.: A lower bound for the smallest eigenvalue of Laplacian. In: Gunning, R. C. (ed.) Problems in analysis, pp. 195–199. Princeton: Princeton University Press 1970

    Google Scholar 

  • [DS] Doyle, P., Snell, J.L.: Random walks and electric networks. Carus Math. Monogr.22, (1984)

  • [DABK] Domany, E., Alexander, S., Bensimon, D., Kadanoff, L.D.: Solution to the Schrödinger equation on some fractal lattices. Phys. Rev., Ser. B28, 3110–3123 (1983)

    Google Scholar 

  • [F] Friedel, M.: Algebraic connectivity of graphs. Czech. Math. J.98, 298–305 (1973)

    Google Scholar 

  • [KSK] Kemeny, J.G., Snell, J.L., Knapp, A.W.: Denumerable Markov chains. Princeton: Nostrand 1966

    Google Scholar 

  • [MW] Mohar, B., Woess, W.: A survey on spectrum of infinite graphs. Università degli studi di Milano, Dipartimento di Matematica “F. Enriques”, Quaderno n. 27/1988

  • [NW] Nash-Williams, C.S.J.A.: Random walks and electric current in networks. Proc. Camb. Phil. Soc.55, 181–194 (1959)

    Google Scholar 

  • [R] Rammal, R.: Spectrum of harmonic excitations on fractals. J. Phys.45, 191–206 (1984)

    Google Scholar 

  • [RT] Rammal, R., Toulouse, T.: Random walks on fractal structures and percolation clusters. J. Phys. Lett.44, 1-13–1-22 (1983)

    Google Scholar 

  • [SW] Soardi, P.M., Woess, W.: Uniqueness of currents in infinite resistive networks. Università degli studi di Milano, Dipartimento di Matematica “F. Enriques”, Quaderno n. 23/1988

  • [T] Telcs, A.: Random walks on graphs, electric networks and fractals. Probab. Th. Rel. Fields82, 435–449 (1989)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Library of the Hungarian Academy of Sciences, P.O. Box 7, H-1361, Budapest, Hungary

    András Telcs

Authors
  1. András Telcs
    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

Telcs, A. Spectra of graphs and fractal dimensions. I. Probab. Th. Rel. Fields 85, 489–497 (1990). https://doi.org/10.1007/BF01203166

Download citation

  • Received: 05 April 1989

  • Revised: 10 October 1989

  • Issue Date: December 1990

  • DOI: https://doi.org/10.1007/BF01203166

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Keywords

  • Stochastic Process
  • Fractal Dimension
  • Probability Theory
  • Mathematical Biology
  • Small Eigenvalue
Download PDF

Working on a manuscript?

Avoid the common mistakes

Advertisement

Search

Navigation

  • Find a journal
  • Publish with us

Discover content

  • Journals A-Z
  • Books A-Z

Publish with us

  • Publish your research
  • Open access publishing

Products and services

  • Our products
  • Librarians
  • Societies
  • Partners and advertisers

Our imprints

  • Springer
  • Nature Portfolio
  • BMC
  • Palgrave Macmillan
  • Apress
  • Your US state privacy rights
  • Accessibility statement
  • Terms and conditions
  • Privacy policy
  • Help and support

167.114.118.210

Not affiliated

Springer Nature

© 2023 Springer Nature