Correlations for the Novak process

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 $B_1, \dots , B_n.$

Keywords

• eynard-mehta theorem
• experimental mathematics and inverse matrices.
• tilings
• non-intersecting lattice paths
• [info.info-dm] computer science [cs]/discrete mathematics [cs.dm]