Journal of Statistical Physics, Vol. 123, No. 5, June 2006, p. 1033-1058.
This paper applies the large deviation technique to a general tree formulation of Generalized Random Energy Model. The similarities and dissimilarities between the exponential and the Gaussian model are discussed. Formulae for limiting free energies, characterization of energy functions are obtained. Limiting case of the tree structure and randomization of the trees are also investigated.