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The Poisson boundary of random rational affinities. (English) Zbl 1087.60011
Summary: We prove that in order to describe the Poisson boundary of rational affinities, it is necessary and sufficient to consider the action on real and all \(p\)-adic fields.

MSC:
60B99 Probability theory on algebraic and topological structures
60G50 Sums of independent random variables; random walks
43A05 Measures on groups and semigroups, etc.
22E35 Analysis on \(p\)-adic Lie groups
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