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Milnor-Wolf theorem for topological groups

I found the following paper: Yves Guivarc'h, Croissance polynomiale et périodes des fonctions harmoniques, Bulletin de la Société Mathématique de France (1973) Volume: 101, page 333-379 The analogou …
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Poisson Furstenberg Boundary of topological groups, reference request

Edit: I found the introduction of this article of A. Furman (mainly quoting results of Furstenberg) useful for one approach to non-amenability, although it maybe isn't quite what you are looking for: …
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