THE LARGE DEVIATION PRINCIPLE FOR MEASURES WITH RANDOM WEIGHTS

In this paper, we study the problem of large deviations for measures w ith random weights. We are motivated by previous work dealing with the special case occuring in the statistical mechanics of the Bose gas. W e study the problem in an abstract setting, isolating what is general from what is dependent on Bose statistics. We succeed in proving the l arge deviation principle for a large class of measures with random wei ghts and obtaining the corresponding rate function in an explicit form . In particular, our results are applicable to the Fermi gas and the s pherical model.