 02265 A. Bovier (WIAS), I. Kurkova (Univ. Paris 6)
 Derrida's Generalized Random Energy models 1:
Models with continuous hierarchies.
(265K, PS)
Jun 13, 02

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Abstract. This is the third of a series of three
papers in which we present a rigorous analysis of Derrida's
Generalized
Random Energy Models (GREM). Here we study the general case
of models with a ``continuum of hierarchies''. We prove the
convergence of the free energy and give
explicite
formulas for the free energy and the tworeplica distribution function.
Then we introduce the empirical distance distribution to
describe effectively the Gibbs measures.
We shhow that its limit is uniquely determined via the
GhirlandaGuerra identities up to the mean of the replica distribution
function.
Finally, we show that suitable
discretizations of the limiting random measure can be described by
the same objects in suitably constructed GREM's.
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