  Models for deterministic quantum mechanics of Cartan-Randers type are
introduced, together with the fundamental notions of the concentration of
measure theory. We explain how the application of the concentration of measure
to Cartan-Randers models provides a framework from which it emerge 1. The
invariance under infinitesimal diffeomorphisms of the macroscopic dynamics 2. A
mechanism for reduction of the quantum state and 3. The Weak Equivalence
Principle.
