GENERIC THINNESS IN FINITELY GENERATED SUBGROUPS OF SLn(Z)
نویسندگان
چکیده
We show that for any n ≥ 2, two elements selected uniformly at random from a symmetrized Euclidean ball of radius X in SLn(Z) will generate a thin free group with probability tending to 1 as X → ∞. This is done by showing that the two elements will form a ping-pong pair, when acting on a suitable space, with probability tending to 1. On the other hand, we give an upper bound less than 1 for the probability that two such elements will form a ping-pong pair in the usual Euclidean ball model in the case where n > 2.
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