Cayley Trees and Bethe Lattices, a concise analysis for mathematicians and physicists

Massimo Ostilli

doi:10.1016/j.physa.2012.01.038

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arXiv · 1109.6725

Cayley Trees and Bethe Lattices, a concise analysis for mathematicians and physicists

Massimo Ostilli

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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.

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Massimo Ostilli. 2012-03-14. Cayley Trees and Bethe Lattices, a concise analysis for mathematicians and physicists. https://doi.org/10.1016/j.physa.2012.01.038

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