Another Poisson boundary description of the flow of weights

Abstract:

A von Neumann algebra is a weakly closed *-subalgebra of the set of bounded operators on a Hilbert space, and a factor is a von Neumann algebra with trivial center. In 1977, Connes-Takesaki associated an ergodic flow to a factor, called the flow of weights, which is a complete isomorphism invariant if the factor is injective of type III. While Krieger showed that every ergodic flow arises from a factor, it is not so easy to describe the flow for a given concrete model. In this talk, I give an overview of attempts to describe it in terms of a Poisson boundary of a random walk.