  We work out the relation between Chern-Simons, 2d Yang-Mills on the cylinder,
and Brownian motion. We show that for the unitary, orthogonal and symplectic
groups, various observables in Chern-Simons theory on S^3 and lens spaces are
exactly given by counting the number of paths of a Brownian particle wandering
in the fundamental Weyl chamber of the corresponding Lie algebra. We construct
a fermionic formulation of Chern-Simons on $S^3$ which allows us to identify
the Brownian particles as B-model branes moving on a non-commutative
two-sphere, and construct 1- and 2-matrix models to compute Brownian motion
ensemble averages.
