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Random subgroups of linear groups are free. (English) Zbl 1239.20051

On an arbitrary finitely generated non-virtually-solvable linear group, any two independent random walks will eventually generate a free subgroup. In fact, this will hold for an exponential number of independent random walks.

MSC:

20G15 Linear algebraic groups over arbitrary fields
20P05 Probabilistic methods in group theory
60G50 Sums of independent random variables; random walks
60B15 Probability measures on groups or semigroups, Fourier transforms, factorization
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