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The Poisson boundary of polycyclic groups. (English) Zbl 0834.60011

Fascicule de probabilités. Séminaire de probabilités, Université de Rennes, France, année 1994. Rennes: Université de Rennes, IRMAR, Publ. Inst. Rech. Math. Rennes. Exp. 3, 14 p. (1994).
Summary: The Poisson boundary for measures with a finite first moment on polycyclic groups is shown to coincide with the corresponding contracting nilpotent Lie group. The proof is based on using a geometric “strip criterion” of boundary maximality due to the author and a simple estimate of the “neutral component” of the random walk.
For the entire collection see [Zbl 0828.00015].

MSC:

60B15 Probability measures on groups or semigroups, Fourier transforms, factorization
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