  We show that the EPRL/FK spin foam model of quantum gravity has an absolutely
convergent partition function if the vertex amplitude is divided by an
appropriate power $p$ of the product of dimensions of the vertex spins. This
power is independent of the spin foam 2-complex and we find that $p>2$ insures
the convergence of the state sum. Determining the convergence of the state sum
for the values $0 \le p \le 2$ requires the knowledge of the large-spin
asymptotics of the vertex amplitude in the cases when some of the vertex spins
are large and other are small.
