Let $F_2$ be the free non-abelian group with generators $a, b\in F_2$.
Has the "random walk" where we start with the identity and then multiply it by $a$ or $b$ or $a^{-1}$ or $b^{-1}$ studied in the literature? Are there any books on it?
Also what about the random walk on the set of finite strings consisting of characters 'a' and 'b' where we start with the empty string then either append a character or remove a character?
