Torsdag, 27 april, 2017, at 16:15-17:00, in Aud. D3 (1531
In 1989, A. Connes and E. J. Woods made a connection between hyperﬁnite von Neumann algebras and Poisson boundaries of time dependent random walks. I will explain this connection and will present two theorems used in their article: the diagrammatic description of almost periodic states on a hyperﬁnite von Neumann algebra (due to A. Connes) and the ergodic decomposition of a Markov measure via harmonic functions (a classical result which can be found in J. Neveu 1964). The crux of the proof of the ﬁrst theorem is a model for conditional expectations on ﬁnite dimensional C*-algebras. Our proof of the second theorem hinges on the notion of cotransition probability.
Kontaktperson: Klaus Thomsen