Coupling functions of domino tilings of Aztec Diamonds
The inverse Kasteleyn matrix of a bipartite graph holds
much information about the perfect matchings of the graph such as its local statistics. These statistics can be used to find global and local asymptotic behavior.
In this talk, we will present three different weightings (one-periodic, two-periodic and qvol weightings) of domino tiling of Aztec diamonds each with different but striking limiting behavior.
We show that it is possible to find recurrence relations which allows a derivation of the inverse Kasteleyn matrix which will hopefully be used in asymptotic computations. This is joint work with Benjamin Young (University of Oregon).