Quenched Large Deviation Principle for the Overlap of a p-Spins System

In this note, we prove a quenched large deviation result for the overlap of a p-spins interaction system at high temperature. The rate function of the large deviation principle is proved to be deterministic, and some of its basic properties are studied. Our result is based on a pure state result for a multidimensional p-spins system combined with a careful application of the Gärtner–Ellis Theorem