  We study the problem of semiclassical limit of Loop Quantum Gravity theory
defined by the new spin foam models. This is done by analyzing the large-spin
asymptotics of the Hartle-Hawking wavefunction. By using the stationary phase
method we determine the wavefunction asymptotics, which then determines the
large-distance asymptotics of the corresponding graviton propagator. We show
that the graviton propagator behaves as the inverse distance to the fourth
power. Our result is a direct consequence of the large-spin asymptotics of the
spin foam model vertex amplitude, and it is valid for all new spin foam models,
since they all have the same type of the vertex amplitude asymptotics. We also
find the type of the vertex amplitude asymptotics which gives the correct
graviton propagator.
