Trapping of random walks on the line

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)n^1/2], where a(c) is given in Eq. (21). (3) The mean-square displacement of a surviving random walker is found to go like n^2/3for 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.