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Explore the multinomial dimer model through this mathematical lecture that extends classical dimer theory to N-dimer covers where every vertex connects to exactly N edges. Learn how this model introduces natural but non-uniform measures on N-dimer covers and discover its remarkable exact solvability in the large N limit across any dimension. Examine the model's properties on lattice subgraphs through the iterated limit process where multiplicity N and graph size both approach infinity, paralleling the scaling limit investigations of 2D standard dimers by Cohn, Kenyon, and Propp. Study explicit computations of limit shapes for specific examples including the Aztec diamond and its 3D analog, the Aztec cuboid. Delve into the comprehensive theoretical framework encompassing explicit free energy formulas, large deviation principles, Euler-Lagrange equations, gauge functions, and regularity properties of limit shapes in this collaborative research with Rick Kenyon.
