Coupling functions for domino tilings of Aztec diamonds

Chhita, Sunil; Young, Benjamin

Abstract

The inverse Kasteleyn matrix of a bipartite graph holds much information about the perfect matchings of the system such as local statistics which can be used to compute local and global asymptotics. In this paper, we consider three different weightings of domino tilings of the Aztec diamond and show using recurrence relations, that we can compute the inverse Kasteleyn matrix. These weights are the one-periodic weighting where the horizontal edges have one weight and the vertical edges have another weight, the qvol weighting which corresponds to multiplying the product of tile weights by q if we add a ‘box’ to the height function and the two-periodic weighting which exhibits a flat region with defects in the center.

Citation

Chhita, S., & Young, B. (2014). Coupling functions for domino tilings of Aztec diamonds. Advances in Mathematics, 259, 173-251. https://doi.org/10.1016/j.aim.2014.01.023

• Journal Article Type: Article
• Acceptance Date: Jan 21, 2014
• Online Publication Date: Apr 3, 2014
• Publication Date: Apr 3, 2014
• Deposit Date: Oct 12, 2016
• Publicly Available Date: Nov 23, 2016
• Journal: Advances in Mathematics
• Print ISSN: 0001-8708
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 259
• Pages: 173-251
• DOI: https://doi.org/10.1016/j.aim.2014.01.023
• Public URL: https://durham-repository.worktribe.com/output/1403002