Nonintersecting random walk in the presence of nonspherical obstacles

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Abstract
The statistics of a self-avoiding walk of N steps on a lattice in a field of asymmetric obstacles is developed. The obstacles are modeled by rigid rods of asymmetry ratio r oriented preferentially and/or by stretched flexible molecules. Each obstacle consists of N segments, each one of which occupies one lattice site. The size, shape, and entropy of the molecule represented by the self-avoiding walk are obtained. The scaling law deviates from the conventional no-obstacles limit (ν=0.6) only for large concentrations of obstacles. However, the molecule is elongated even for a small concentration of obstacles. Because the formulas are so easily obtained and extended the method promises to be widely applicable.

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