Asymptotics of 6j and 10j symbols

It is well known that the building blocks for state sum models of quantum gravity are given by 6j and 10j symbols. In this work, we study the asymptotics of these symbols by using their expressions as group integrals. We carefully describe the measure involved in terms of invariant variables and develop new technics in order to study their asymptotics. Using these technics, we compute the asymptotics of the various Euclidean and Lorentzian 6j symbols. Finally, we compute the asymptotic expansion of the 10j symbol which is shown to be non-oscillating, in agreement with a recent result of Baez et al. We discuss the physical origin of this behaviour and a way to modify the Barrett-Crane model in order to cure this disease.