Samenvatting:
In this lecture we start by explaining the classification theory for
classical (commutative) Bernoulli schemes, which are special examples
of "purely random" dynamical systems. Next we discuss their noncommutative
versions, which are von Neumann algebras together with specially defined
*-isomorphisms. Noncommutative Bernoulli schemes are models for spatially
infinite quantum spin systems.Finally, we sketch two proofs for homomorphism
theorems for the noncommutative versions, following a joint article with
T. Hamachi, and state the open problem of classification of these objects
up to isomorphism.