Polymer topology — how many times does a chain wind around a point?
The winding number of a 2D random walk around the origin counts how many times the path winds around the pole. For a continuous planar Brownian motion up to time T, the winding number W(T) has characteristic function E[e^{iθW}] ∝ (log T)^{−θ²/2}, meaning W(T)/√(½ log T) → N(0,1) (Spitzer 1958). Polymer models use winding to study topological entanglement.