A train track directed random walk on $Out(F_r)$

Ilya Kapovich, Catherine Pfaff

Several known results, by Rivin, Calegari-Maher and Sisto, show that an element ${\varphi }_n\in Out(F_r)$, obtained after $n$ steps of a simple random walk on $Out(F_r)$, is fully irreduci…