  We study a model for the entanglement of a two-dimensional reflecting
Brownian motion in a bounded region divided into two halves by a wall with
three or more small windows. We map the Brownian motion into a Markov Chain on
the fundamental groupoid of the region. We quantify entanglement of the path
with the length of the appropriate element in this groupoid. Our main results
are a law of large numbers and a central limit theorem for this quantity. The
constants appearing in the limit theorems are expressed in terms of a coupled
system of quadratic equations.
