  We develop a unified theory to analyze the microcanonical ensembles with
several constraints given by unbounded observables. Several interesting
phenomena that do not occur in the single constraint case can happen under the
multiple constraints case. We systematically analyze the detailed structures of
such microcanonical ensembles in two orthogonal directions using the theory of
large deviations. First of all, we establish the equivalence of ensembles
result, which exhibits an interesting phase transition phenomenon. Secondly, we
study the localization and delocalization phenomena by obtaining large
deviation results for the joint law of empirical distributions and the maximum
component. Some concrete examples for which the theory applies will be given as
well.
