The well-known "Arctic Circle Theorem" states that uniformly random domino tilings (matchings) of an Aztec diamond of high order are frozen outside the “arctic circle” inscribed within the diamond, with asymptotically high probability. In this project, we plan to study maximal weight perfect matching on a sequence of growing planar bipartite graphs (on square or triangular lattice), like the Aztec diamond, with random edge-weights and find their asymptotic behavior. We will use Hungarian method to find the maximal matching and visualize them using standard coloring scheme (for square lattice) or surface representation (for triangular lattice). Strong coding ability (Matlab or Python) is required. [Image published at de.wikipedia.org by user MiaFr under the Creative Commons Attribution-Share Alike 3.0 Unported License.]
Completion of Calculus 3. Knowledge of Graph Theory and coding in Matlab or Python is required.