Szegö asymptotcs for Angelesco systems

We discuss opportunity for extension the strong asymptotics (Szegö asymptotics) for more wide class of the sequences of multiple orthogonal polynomials with respect to the system of weights supported by the non-intersecting intervals (Angelesco system). The interest for limiting properties of these polynomials, when their multi-index tends monotonically to infinity (along of the edges of $p$-dimensional lattice) has appeared recently, in onnection with spectral problems for the discrete Schrodinger operator (multidimensional Jacobi matrix) on the graph-trees.