Journal of Statistical Physics

, Volume 133, Issue 3, pp 513–533

On the Validations of the Asymptotic Matching Conjectures

  • S. Friedland
  • E. Krop
  • P. H. Lundow
  • K. Markström
Article

Abstract

In this paper we review the asymptotic matching conjectures for r-regular bipartite graphs, and their connections in estimating the monomer-dimer entropies in d-dimensional integer lattice and Bethe lattices. We prove new rigorous upper and lower bounds for the monomer-dimer entropies, which support these conjectures. We describe a general construction of infinite families of r-regular tori graphs and give algorithms for computing the monomer-dimer entropy of density p, for any p∈[0,1], for these graphs. Finally we use tori graphs to test the asymptotic matching conjectures for certain infinite r-regular bipartite graphs.

Keywords

Matching and asymptotic growth of average matchings for r-regular bipartite graphs Monomer-dimer partitions and entropies 

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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • S. Friedland
    • 1
    • 2
  • E. Krop
    • 1
  • P. H. Lundow
    • 3
  • K. Markström
    • 4
  1. 1.Department of Mathematics, Statistics and Computer ScienceUniversity of Illinois at ChicagoChicagoUSA
  2. 2.Berlin Mathematical SchoolBerlinGermany
  3. 3.Department of PhysicsAlbaNova University CenterStockholmSweden
  4. 4.Department of Mathematics and Mathematical StatisticsUmeå UniversityUmeåSweden

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