THE CLOSURE OF A RANDOM BRAID IS A HYPERBOLIC LINK.

Let μ be a probability distribution on the braid group Bn with n ≥3 strands. We observe that for a random walk ωn,k of length k on Bn, the probability that the closure ωn,k is a hyperbolic link in S³ converges to 1 as k tends to infinity. Moreover, under a mild assumption on μ, we prove the probability that the closure ωn,k is a hyperbolic knot which has no nontrivial exceptional surgeries is larger than zero for k large enough. The proofs combine several recent deep results. [ABSTRACT FROM AUTHOR]