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- W2963426048 abstract "We show that for any $ngeq 2$, two elements selected uniformly at random from a emph{symmetrized} Euclidean ball of radius $X$ in $textrm{SL}_n(mathbb Z)$ will generate a thin free group with probability tending to $1$ as $Xrightarrow infty.$ 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 $n>2$." @default.
- W2963426048 created "2019-07-30" @default.
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- W2963426048 date "2016-08-05" @default.
- W2963426048 modified "2023-09-24" @default.
- W2963426048 title "Generic Thinness in Finitely Generated Subgroups of SL$_n(mathbb Z)$" @default.
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- W2963426048 doi "https://doi.org/10.1093/imrn/rnw136" @default.
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