  We prove that the asymptotic of the bulk local statistics in models of random
lozenge tilings is universal in the vicinity of straight boundaries of the
tiled domains. The result applies to uniformly random lozenge tilings of large
polygonal domains on triangular lattice and to the probability measures
describing the decomposition in Gelfand-Tsetlin bases of tensor products of
representations of unitary groups. In a weaker form our theorem also applies to
random domino tilings.
