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Bulk Universality for Random Lozenge Tilings Near Straight Boundaries and for Tensor Products

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, USA

    Vadim Gorin

  2. Institute for Information Transmission Problems of Russian Academy of Sciences, Moscow, Russia

    Vadim Gorin

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  1. Vadim Gorin
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Correspondence to Vadim Gorin.

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Communicated by A. Borodin

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Gorin, V. Bulk Universality for Random Lozenge Tilings Near Straight Boundaries and for Tensor Products. Commun. Math. Phys. 354, 317–344 (2017). https://doi.org/10.1007/s00220-016-2801-x

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