Non-intersecting paths and Hahn orthogonal polynomial ensemble

TL;DR

This paper analyzes the asymptotic behavior of lozenge tilings of a hexagon, revealing a limiting process related to the discrete sine process that describes the system's bulk correlations.

Contribution

It computes the bulk limit of correlation functions for lozenge tilings, identifying a new translation invariant process extending the discrete sine process.

Findings

Bulk correlation functions converge to a translation invariant process

Limiting process extends the discrete sine process

Describes ergodic Gibbs measure for tilings

Abstract

We compute the bulk limit of the correlation functions for the uniform measure on lozenge tilings of a hexagon. The limiting determinantal process is a translation invariant extension of the discrete sine process, which also describes the ergodic Gibbs measure of an appropriate slope.