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Coupling functions for domino tilings of Aztec diamonds.

Chhita, Sunil and Young, Benjamin (2014) 'Coupling functions for domino tilings of Aztec diamonds.', Advances in mathematics., 259 . pp. 173-251.

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.

Item Type:Article
Full text:(AM) Accepted Manuscript
Available under License - Creative Commons Attribution Non-commercial No Derivatives.
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1016/j.aim.2014.01.023
Publisher statement:© 2014 This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Date accepted:21 January 2014
Date deposited:23 November 2016
Date of first online publication:03 April 2014
Date first made open access:No date available

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