RANDOM WALKS ON BRATTELI DIAGRAMS

Jean N Renault (1)

1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans

In a 1989 article, 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 given there: the description of an almost periodic state on a hyperfinite von Neumann algebra (due to A. Connes) and the ergodic decomposition of a Markov measure via harmonic functions (a classical result in J. Neveu 64). The crux 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.

Mots clés: Bratteli diagrams; hyperfinite von Neumann algebras; Markov measures

Domaines: Algèbres d'opérateurs [math.OA]

Jean N Renault. RANDOM WALKS ON BRATTELI DIAGRAMS. 2017. ⟨hal-01514270⟩