  The Littlewood-Richardson coefficients describe the decomposition of tensor
products of irreducible representations of a simple Lie algebra into
irreducibles. Assuming the number of factors is large, one gets a measure on
the space of weights. This limiting measure was extensively studied by many
authors. In particular, Kerov computed the corresponding density in a special
case in type A and Kuperberg gave a formula for the general case. The goal of
this paper is to give a short, self-contained and pure Lie theoretic proof of
the formula for the density of the limiting measure. Our approach is based on
the link between the limiting measure induced by the Littlewood-Richardson
coefficients and the measure defined by the weight multiplicities of the tensor
products.
