Distortion for Abelian Subgroups of $\mathrm{O}\mathrm{u}\mathrm{t}(F_n)$

We prove that abelian subgroups of the outer automorphism group of a free group are quasi-isometrically embedded. Our proof uses recent developments in the theory of train track maps by Feighn-Handel. As an application, we prove the rank conjecture for $\mathrm{O}\mathrm{u}\mathrm{t}(F_n)$.