Abstract In this paper we investigate the distribution function of available options for the final step of self-avoiding walks (SAWs) on various lattices. The asymptotic fraction of walks with j legal options at the last step equals the fraction of walks with ( q − j − 1 ) contacts at the origin, where q is the lattice coordination number. We present a method to estimate these fractions by exploiting their weak dependence on walk length for n > k + 2 , where k is the step at which the last contact with the origin occurs. Numerical results are provided for five distinct lattices using three methods: extrapolation of exact enumerations, Monte Carlo simulations, and the maximum entropy method (MEM). The MEM is inspired by the evident correspondence between SAWs and statistical physics, where entropy plays a fundamental role. Despite the lack of rigorous justification, the MEM yields reasonably accurate approximations. This study presents new methods for the analysis of SAWs and provides information about the local structure of SAWs on several lattices.
Baram et al. (Fri,) studied this question.
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