  Using a general Green function formulation, we re-derive, both, (i) Spitzer
and his followers results for the winding angle distribution of the planar
Brownian motion, and (ii) Edwards-Prager-Frisch results on the statistical
mechanics of a ring polymer entangled with a straight bar. In the statistical
mechanics part, we consider both cases of quenched and annealed topology. Among
new results, we compute exactly the (expectation value of) the surface area of
the locus of points such that each of them has linking number $n$ with a given
closed random walk trajectory ($=$ ring polymer). We also consider the
generalizations of the problem for the finite diameter (disc-like) obstacle and
winding within a cavity.
