Coupling functions for domino tilings of Aztec diamonds
2014 (English)In: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 259, 173-251 p.Article in journal (Refereed) Published
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 q(vol) 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.
Place, publisher, year, edition, pages
2014. Vol. 259, 173-251 p.
Aztec diamond, Kasteleyn matrix, Dimer, Domino tilings
IdentifiersURN: urn:nbn:se:kth:diva-146125DOI: 10.1016/j.aim.2014.01.023ISI: 000335717400008ScopusID: 2-s2.0-84897391303OAI: oai:DiVA.org:kth-146125DiVA: diva2:722956
FunderKnut and Alice Wallenberg Foundation, KAW 2010:0063
QC 201406102014-06-102014-06-092014-06-10Bibliographically approved