  We present an interesting connection between Brownian motion and magnetism.
We use this to determine the distribution of areas enclosed by the path of a
particle diffusing on a sphere. In addition, we find a bound on the free energy
of an arbitrary system of spinless bosons in a magnetic field. The work
presented here is expected to shed light on polymer entanglement, depolarized
light scattering, and magnetic behavior of spinless bosons.
