1109.6725 (Massimo Ostilli)

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

Massimo Ostilli

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.

View original: http://arxiv.org/abs/1109.6725