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Mean-Field Monomer-Dimer Models. A Review

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Sojourns in Probability Theory and Statistical Physics - I

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 298))

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Abstract

A collection of rigorous results for a class of mean-field monomer-dimer models is presented. It includes a Gaussian representation for the partition function that is shown to considerably simplify the proofs. The solutions of the quenched diluted case and the random monomer case are explained. The presence of the attractive component of the Van der Waals potential is considered and phase transition analysed. In particular the breakdown of the central limit theorem is illustrated at the critical point where a non Gaussian, quartic exponential distribution is found for the number of monomers centered and rescaled with the volume to the power 3/4.

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Notes

  1. 1.

    For example one can choose \(w_{ii}\ge \sum _{j\ne i}w_{ij}\) for every \(i=1,\dots ,N\).

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Authors and Affiliations

  1. Department of Mathematics, University of Bologna, Piazza di Porta San Donato 5, Bologna, Italy

    Diego Alberici, Pierluigi Contucci & Emanuele Mingione

Authors
  1. Diego Alberici
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  2. Pierluigi Contucci
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  3. Emanuele Mingione
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Corresponding author

Correspondence to Pierluigi Contucci .

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Editors and Affiliations

  1. NYU Shanghai, Shanghai, China

    Vladas Sidoravicius

Additional information

To Chuck Newman, on his 70th birthday.

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Alberici, D., Contucci, P., Mingione, E. (2019). Mean-Field Monomer-Dimer Models. A Review. In: Sidoravicius, V. (eds) Sojourns in Probability Theory and Statistical Physics - I. Springer Proceedings in Mathematics & Statistics, vol 298. Springer, Singapore. https://doi.org/10.1007/978-981-15-0294-1_2

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