A result of Malyutin shows that a random walk on the mapping class group gives rise to an element whose fractional Dehn twist coefficient is large or small enough. We show that this leads to several properties of random 3-manifolds and links. For example, random closed braids and open books are hyperbolic.
"On a structure of random open books and closed braids." Proc. Japan Acad. Ser. A Math. Sci. 91 (10) 160 - 162, December 2015. https://doi.org/10.3792/pjaa.91.160