A short description of our research topic, and why it is important to modern mathematics.
Random tilings of planar regions have been studied by a number of people in the 1990's and 2000's for various reasons. Our approach is to find recursions satisfied by various quantities: the number of weighted tilings or "partition function", the probabilities of certain local configurations, as well as certain other quantities known as "creation rates", "deficits", etc.
We will also take advantage of known relationships between tilings and objects: trees, height functions, matchings, Pfaffian determinants, determinental processes, Kastelyn matrices and Dodgson condensation, to name a few.
Utilizing computer programs capable of calculations beyond human ability, we are able to see patterns that arise from applying known algorithms to vast matrices.