Journal of Theoretical Probability

, Volume 8, Issue 2, pp 453–473 | Cite as

On the range of reversible random walks onZ2 in a random environment

  • Xian Yin Zhou
Article

Abstract

In this paper, a weak law of large numbers is obtained for the range of two dimensional reversible random walk in a random environment.

Key Words

Law of large numbers range random walk hitting time effective resistance 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Barlow, M. T., and Bass, R. F. (1989). The construction of Brownian motion on the Sierpinski carpet,Ann. Inst. Herni. Poincare 25, 225–257.Google Scholar
  2. 2.
    Barlow M. T., and Bass, R. F. (1992). Transition densities for the Brownian motion on the Sierpinski carpet,Probab. Th. Rel. Fields 92.Google Scholar
  3. 3.
    Doyle, P. G., and Snell, J. L. (1984). Random Walks and Electric Networks, The Carus Math. Monographs, Washington DC.Google Scholar
  4. 4.
    Le Gall, J. F., and Rosen, J. (1991). The range of stable random walks,Ann. Prob. 19, 650–705.Google Scholar
  5. 5.
    De Masi, A., Ferrari, P. A., Goldstein, S., and Wick, W. D. (1989). An invariance principle for reversible Markov process: Applications to random motion in random environment,J. Stat. Phys. 55, 787–855.Google Scholar
  6. 6.
    Telcs, A. (1989). Random walks on graphs, electric networks and fractals,Prob. Th. rel. Fields 82, 435–449.Google Scholar
  7. 7.
    Zhou, X. Y. (1993). Green function estimates and their applications to the intersections of symmetric random walks,Stoch. Proc. Appl. 48, 31–60.Google Scholar

Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • Xian Yin Zhou
    • 1
  1. 1.Department of MathematicsBeijing Normal UniversityBeijingP. R. China

Personalised recommendations