Winding-Angle Distributions of Two-Dimensional Self-Avoiding Walks from Conformal Invariance

Abstract

We derive the exact probability distribution of the winding angle of a two-dimensional self-avoiding walk around its extremities, using Coulomb-gas techniques and conformal invariance. This gives a first example of an exact full distribution in critical geometrical models. It is extended to dense and $\Theta$ self-avoiding walks.