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• W2964113767 abstract "In this note, we prove that a random extension of either the free group |$F_N$| of rank |$Nge 3$| or of the fundamental group of a closed, orientable surface |$S_g$| of genus |$gge 2$| is a hyperbolic group. Here, a random extension is one corresponding to a subgroup of either |${rm Out}(F_N)$| or |${rm Mod}(S_g)$| generated by |$k$| independent random walks. Our main theorem is that a |$k$|-generated random subgroup of |${rm Mod}(S_g)$| or |${rm Out}(F_N)$| is free of rank |$k$| and convex cocompact. More generally, we show that a |$k$|-generated random subgroup of a weakly hyperbolic group is free and undistorted.Communicated by Prof. Igor Rivin" @default.
• W2964113767 created "2019-07-30" @default.
• W2964113767 creator A5039880499 @default.
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• W2964113767 date "2015-05-14" @default.
• W2964113767 modified "2023-09-26" @default.
• W2964113767 title "Random Extensions of Free Groups and Surface Groups are Hyperbolic" @default.
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• W2964113767 doi "https://doi.org/10.1093/imrn/rnv138" @default.
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