  We consider a set of measures on the real line and the corresponding system
of multiple orthogonal polynomials (MOPs) of the first and second type. Under
some very mild assumptions, which are satisfied by Angelesco systems, we define
self-adjoint Jacobi matrices on certain rooted trees. We express their Green's
functions and the matrix elements in terms of MOPs. This provides a
generalization of the well-known connection between the theory of polynomials
orthogonal on the real line and Jacobi matrices on $\mathbb{Z}_+$ to higher
dimension. We illustrate importance of this connection by proving ratio
asymptotics for MOPs using methods of operator theory.
