Anyon model, axial anomaly and planar brownian winding

Abstract

We consider various topics related to the anyon model: i) the computation for a gas of anyons of the second virial coefficient a 2 ii) the relation of the latter to the 1+1 dimensional axial anomaly iii) the derivation of the probability P( n) for a planar brownian curve to wind n times around a given point as the Fourier transform of a 2. We then study the joint probability P( n, A) for the curve to wind n times and enclose an algebraic aera A.