Probabilistic Derivation of a Noncommutative Version of Varadhan's Theorem

We give a simple probabilistic derivation of a special case of a noncommutative version of Varadhan's theorem, first proved by Petz, Raggio and Verbeure. It is based on a Feynman-Kac representation combined with a standard large deviation argument. In the final section, this theorem is then extended to a more difficult situation with Bose symmetry.