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Random walks on Bratteli diagrams.

Jean Renault
(Universite d'Orleans)
Analysis Seminar
Thursday, 27 April, 2017, at 16:15-17:00, in Aud. D3 (1531-215)
Abstract:
 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.
Contact person: Klaus Thomsen
89566 / i31