# Asymptotics of random lozenge tilings via Gelfand–Tsetlin schemes

@article{Petrov2012AsymptoticsOR, title={Asymptotics of random lozenge tilings via Gelfand–Tsetlin schemes}, author={Leonid A. Petrov}, journal={Probability Theory and Related Fields}, year={2012}, volume={160}, pages={429-487} }

A Gelfand–Tsetlin scheme of depth $$N$$N is a triangular array with $$m$$m integers at level $$m$$m, $$m=1,\ldots ,N$$m=1,…,N, subject to certain interlacing constraints. We study the ensemble of uniformly random Gelfand–Tsetlin schemes with arbitrary fixed $$N$$Nth row. We obtain an explicit double contour integral expression for the determinantal correlation kernel of this ensemble (and also of its $$q$$q-deformation). This provides new tools for asymptotic analysis of uniformly random… Expand

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