  We provide a probabilistic approach to studying minimal surfaces in
three-dimensional Euclidean space. Following a discussion of the basic
relationship between Brownian motion on a surface and minimality of the
surface, we introduce a way of coupling Brownian motions on two minimal
surfaces. This coupling is then used to study two classes of results in the
theory of minimal surfaces, maximum principle-type results, such as weak and
strong halfspace theorems and the maximum principle at infinity, and Liouville
theorems.
