The winding angle distribution of an ordinary random walk

Abstract

The winding angle about a selected point of a random walk quantifies what is perhaps the simplest manifestation of entanglement a phenomenon of great importance in the study of polymers. The distribution of winding angles is studied here for ordinary or non-self-avoiding walks. New results highlight the crucial influence of the exclusion of a finite region about the selected point on the winding angle distribution. The results of this analysis are compared with simulations of random walks on a lattice, the agreement between the two is very good. There are, however, small and as yet unexplained discrepancies.