Chhita, Sunil and Young, Benjamin (2014) 'Coupling functions for domino tilings of Aztec diamonds.', Advances in mathematics., 259 . pp. 173-251.
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.
|Full text:||(AM) Accepted Manuscript|
Available under License - Creative Commons Attribution Non-commercial No Derivatives.
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|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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