Cayley Trees and Bethe Lattices: A concise analysis for mathematicians and physicists

M. Ostilli

Physica A: Statistical Mechanics and its Applications, 2012, vol. 391, issue 12, 3417-3423

Abstract: We review critically the concepts and the applications of Cayley Trees and Bethe Lattices in statistical mechanics in a tentative effort to remove widespread misuse of these simple, but yet important–and different–ideal graphs. We illustrate, in particular, two rigorous techniques to deal with Bethe Lattices, based respectively on self-similarity and on the Kolmogorov consistency theorem, linking the latter with the Cavity and Belief Propagation methods, more known to the physics community.

Keywords: Rigorous results in statistical mechanics; Solvable lattice models; Exact results; Message-passing algorithms (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:391:y:2012:i:12:p:3417-3423

DOI: 10.1016/j.physa.2012.01.038

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