Copyright © 2011 Kangkang Wang and Decai Zong. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
A class of small-deviation theorems for the relative entropy densities
of arbitrary random field on the generalized Bethe tree are discussed by comparing
the arbitrary measure with the Markov measure on the generalized Bethe tree.
As corollaries, some Shannon-Mcmillan theorems for the arbitrary random field on the
generalized Bethe tree, Markov chain field on the generalized Bethe tree are obtained.