Asymptotics of random lozenge tilings via Gelfand–Tsetlin schemes

A Gelfand–Tsetlin scheme of depth N is a triangular array with m integers at level m , m = 1 , … , N , subject to certain interlacing constraints. We study the ensemble of uniformly random Gelfand–Tsetlin schemes with arbitrary fixed N th row. We obtain an explicit double contour integral expression...

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