Bulk universality for random lozenge tilings near straight boundaries and for tensor products

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.

27 pages, 11 figures. v2: inconsistency in Section 4 notations corrected

References in corpus (3)

• Fluctuations of particle systems determined by Schur generating functions
• Fixed energy universality for generalized Wigner matrices
• On Universality of Bulk Local Regime of the Deformed Gaussian Unitary Ensemble

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