Central limit theorems in disordered Monomer-Dimer model

Given a finite graph, one puts i.i.d. weights on the edges and i.i.d. weights on the vertices. For a (partial) matching on this graph, define the weight of the matching by adding all the weights of the edges in the matching (corresponding to the energy of dimers) together with the weights of the unmatched vertices (energy of monomers). In the disordered monomer-dimer model, one is interested in the associated Gibbs measure. We prove Gaussian central limit theorems for the free energy associated to the Gibbs measure and also the Gibbs average of the number of dimers as the size of the graph tends to infinity. Our proof relies on the idea that the disordered monomer-dimer model exhibits a decay of correlation with high probability. Joint work with Arnab Sen (Minnesota).