  In this paper, we study the structure of a family of superposition states on
tensor algebras. The correlation functions of the considered states are
described through a new kind of positive definite kernels valued in the dual of
C$^\ast$-algebras, so-called Schur kernels. Mainly, we show the existence of
the limiting state of a net of superposition states over an arbitrary locally
finite graph. Furthermore, we show that this limiting state enjoys a mixing
property and an $\alpha$-mixing property in the case of the multi-dimensional
integer lattice $\mathbb{Z}^\nu$.
