Journal of Statistical Physics

, Volume 15, Issue 5, pp 393–397 | Cite as

A simple calculation for the average number of steps to trapping in lattice random walks

  • Kurt E. Shuler
  • Howard Silver
  • Katja Lindenberg


We show that the asymptotic results for the average number of steps to trapping at an irreversible trapping site on aD-dimensional finite lattice can be obtained from the generating function for random walks on aninfinite perfect lattice. This introduces a significant simplification into such calculations. An interesting corollary of these calculations is the conclusion that a random walker traverses, on the average, all the distinct nontrapping lattice sites before arriving on the trapping site.

Key words

Random walk steps to trapping lattice walk 


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  1. 1.
    E. W. Montroll,J. Math. Phys. 10:753 (1969).Google Scholar
  2. 2.
    K. Lakatos-Lindenberg and K. E. Shuler,J. Math. Phys. 12:637 (1971).Google Scholar
  3. 3.
    R. P. Hemenger, R. M. Pearlstein, and K. Lakatos-Lindenberg,J. Math. Phys. 12:1056 (1971).Google Scholar
  4. 4.
    G. Hoch and R. S. Knox, inPhotophysiology, A. Giese, ed., Academic, New York (1968), Vol. 3; R. S. Knox, inBioenergetics of Photosynthesis, Govindjee, ed., Academic Press, New York (1975).Google Scholar
  5. 5.
    J. B. Birks,J. Phys. B 3:1704 (1970); D. Haarer and H. Wolf,Mol. Cryst. Liq. Cryst. 10:359 (1970); J. B. Birks, inOrganic Molecular Photophysics, J. B. Birks, ed., Wiley, New York (1975), Vol. 2.Google Scholar
  6. 6.
    R. B. Fox, T. R. Price, and R. F. Cozzens,J. Chem. Phys. 54:79 (1971).Google Scholar
  7. 7.
    E. W. Montroll and G. H. Weiss,J. Math. Phys. 6:167 (1965).Google Scholar
  8. 8.
    H. B. Rosenstock,J. Math. Phys. 11:487 (1970).Google Scholar

Copyright information

© Plenum Publishing Corporation 1976

Authors and Affiliations

  • Kurt E. Shuler
    • 1
  • Howard Silver
    • 1
  • Katja Lindenberg
    • 1
  1. 1.Department of ChemistryUniversity of California-San DiegoLa Jolla

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