Survival probability arguments have been developed for obtaining generalized formulas for the end-to-end distance exponents of the self-avoiding walk, the kinetic growth walk (KGW), and the true self-avoiding walk on a percolating cluster. A crossover in the asymptotic behavior of KGW on a two dimensional percolating cluster has been observed at a walk length [approx equals] 60. This is presented as numerical evidence of the fact that the KGW latches onto a backbone as it grows longer.
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