Trapping of random walks on the line

George H. Weiss, Shlomo Havlin

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57 Scopus citations


Several features of the trapping of random walks on a one-dimensional lattice are analyzed. The results of this investigation are as follows: (1) The correction term to the known asymptotic form for the survival probability to n steps is O((λ2n)-1/3), where λ=-ln(1-c), and c is the trap concentration. (2) The short time form for the survival probability is found to be exp[-a(c)n1/2], where a(c) is given in Eq. (21). (3) The mean-square displacement of a surviving random walker is found to go like n2/3for large n. (4) When the distribution of trap-free regions is changed so that very large regions are much rarer than for ideally random trap placement the asymptotic survival probability changes its dependence on n. One such model is studied.

Original languageEnglish
Pages (from-to)17-25
Number of pages9
JournalJournal of Statistical Physics
Issue number1-2
StatePublished - Oct 1984
Externally publishedYes


  • Random walks
  • diffusion
  • survival probabilities
  • trapping


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