  Recently, a proposal has appeared for the extraction of the 2-point function
of linearised quantum gravity, within the spinfoam formalism. This relies on
the use of a boundary state, which introduces a semi-classical flat geometry on
the boundary. In this paper, we investigate this proposal considering a toy
model in the (Riemannian) 3d case, where the semi-classical limit is better
understood. We show that in this limit the propagation kernel of the model is
the one for the harmonic oscillator. This is at the origin of the expected 1/L
behaviour of the 2-point function. Furthermore, we numerically study the short
scales regime, where deviations from this behaviour occur.
