Solution of the monomer-dimer model on locally tree-like graphs. Rigorous results

Abstract

We consider the monomer-dimer model on sequences of random graphs locally convergent to trees. We prove that the monomer density converges almost surely, in the thermodynamic limit, to an analytic function of the monomer activity. We characterise this limit as the expectation of the solution of a fixed point distributional equation and we give an explicit expression for the limiting pressure per particle.

33 pages, 2 figures. Improved results and citations added with respect to the previous version

References in corpus (3)

• Ising models on locally tree-like graphs
• The number of matchings in random graphs
• A rigorous proof of the cavity method for counting matchings

Cited by in corpus (8)

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• A mean-field monomer-dimer model with random monomer activities. Exact solution and rigorous results
• Disordered Monomer-Dimer model on Cylinder graphs
• Two populations mean-field monomer-dimer model
• Matchings on Random Regular Hypergraphs
• Finite-size corrections for the attractive mean-field monomer-dimer model