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

► Review Paper: Cayley Tree and Bethe Lattice are essential concepts in Stat. Mech. ► Misuses and serious misunderstandings are still very common in the Literature. ► We critically review definitions, properties and techniques for CT and BL models. ► For BL we illustrate two techniques: Self-Similarity and the Kolmogorov theorem. ► Kolmogorov theorem leads to a rigorous derivation of the Belief-Propagation Eqs.