Trapping of genuine self-avoiding walks

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Abstract
It is shown that, depending upon the lattice, there are two different trapping mechanisms for a genuine self-avoiding walk (GSAW), also called kinetic growth walk. Normal trapping, which may occur anywhere on the lattice, occurs with probability one and with a finite value for the average walk length. Abnormal trapping, exemplified by GSAW on a two-dimensional oriented square lattice, requires return to the neighborhood of the starting point, and occurs (we conjecture) with probability one but with infinite average walk length. The walk length distribution and the distribution of trapped walkers are provided for GSAW on the square lattice, and for 2-tolerant GSAW in one dimension. In the latter case the average walk length is 25 steps, and the average displacement of a trapped walker from his starting point is ten lattice spacings.

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