  It is shown that Parisi-Sourlas supersymmetry of stochastic quantization is a
Cartan model of equivariant cohomology. Equivariant cohomological structure of
stochastic quantization of linear and non-linear sigma models are discussed.
Witten's nonabelian localization principle is applied to the stochastic
quantization of matrix models. As a result the equivalence between the original
matrix model and the corresponding quenched Eguchi-Kawai model is established.
