Large Deviations and Variational Theorems for Marginal Problems
February 1995
       P. Cattiaux
       Ecole Polytechnique, CMAP, F-91128 Palaiseau Cedex
       and 
       Universite Paris X 
       equipe MODAL'X Nanterre 200
       avenue de la republique F-92001 Nanterre Cedex.
       email: cattiaux@paris.polytechnique.fr
 and
       F.Gamboa
       Laboratoire de Statistiques Universit{e} Paris Sud
       F-91405 Orsay  and Universit{e} Paris-Nord
       Institut Galil{e}e F-93430 Villetaneuse. email:
       gamboa@stats.matups.fr}}

 Summary:
On a product Probability space , we give variational
characterizations for the existence of a Probability measure Q
with given marginals, such that Q is absolutely continuous
with respect to P, and its density satisfies some integrability
conditions.


These characterizations, which are in some sense the dual
formulation of a Theorem of Strassen , are obtained
by using large deviations methods. We also study the minimal
realizations of such Q.

 Key words: Marginal Problems-Large Deviations}


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