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

TL;DR

This paper demonstrates that local statistical behavior in large random lozenge tilings near straight boundaries is universal, extending to tensor product decompositions and domino tilings under certain conditions.

Contribution

It establishes a universal bulk local statistics result for random lozenge tilings and related models, including tensor product measures and domino tilings.

Findings

Universal bulk local statistics near straight boundaries.

Applicability to large polygonal domains and tensor product measures.

Extension to random domino tilings in a weaker form.

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.