Please note special time.  We study the decompositions into irreducible components of tensor products and restrictions of irreducible representations of classical Lie groups as the rank of the group goes to infinity. We prove the Law of Large Numbers for the random counting measures describing the decomposition. Connections of this result with free probability, random lozenge tilings, and extreme characters of the infinite-dimensional unitary group will be explained.  The talk is based on joint works with A. Borodin, V. Gorin, and G. Olshanski.