Expected Depth of Random Walks on Groups

Khalid bou-Rabee, Ioan Manolescu, Aglaia Myropolska

For $G$ a finitely generated group and $g\in G$, we say $g$ is detected by a normal subgroup $N⊲G$ if $g\notin N$. The depth $D_G(g)$ of $g$ is the lowest index of a normal,…