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Kesav Krishnan / Disordered Monomer Dimer Models on Cylinder Graphs
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"Disordered Monomer Dimer Models on Cylinder Graphs"
Abstract: I will introduce the notion of Monome-Dimer Models, that is the study of randomly sampled matchings on Graphs. I will briefly survey previously known results, and then describe joint work with Partha Dey. We analyse the model on a family of psuedo-one dimensional graphs we refer to as cylinder graphs, with independent and identically distributed random weights on both the edges and vertices. We establish convergence and a Gaussian central limit theorem for the mean free energy, and also prove central limit theorems for the scaled number of unpaired vertices in a typical matching. Finally, we place matchings in correspondence with increasing functions defined on an interval, and establish distributional convergence to Brownian Motion.
Abstract: I will introduce the notion of Monome-Dimer Models, that is the study of randomly sampled matchings on Graphs. I will briefly survey previously known results, and then describe joint work with Partha Dey. We analyse the model on a family of psuedo-one dimensional graphs we refer to as cylinder graphs, with independent and identically distributed random weights on both the edges and vertices. We establish convergence and a Gaussian central limit theorem for the mean free energy, and also prove central limit theorems for the scaled number of unpaired vertices in a typical matching. Finally, we place matchings in correspondence with increasing functions defined on an interval, and establish distributional convergence to Brownian Motion.