Correlations for the Novak process

TL;DR

This paper analyzes the correlation functions of random lozenge tilings of the Novak half-hexagon, revealing similarities with Aztec diamond domino tilings and involving complex matrix inversion techniques.

Contribution

It provides the first computation of correlation functions for the Novak process and introduces methods for inverting specific binomial coefficient matrices.

Findings

Correlation functions for the Novak process are explicitly computed.

The model shows intriguing similarities with Aztec diamond tilings.

A novel matrix inversion technique for binomial coefficient matrices is developed.

Abstract

We study random lozenge tilings of a certain shape in the plane called the Novak half-hexagon, and compute the correlation functions for this process. This model was introduced by Nordenstam and Young (2011) and has many intriguing similarities with a more well-studied model, domino tilings of the Aztec diamond. The most difficult step in the present paper is to compute the inverse of the matrix whose (i,j) entry is the binomial coefficient C(A, B_j - i) for indeterminate variables A and B_1, ..., B_n.