3 problems

Let ${\cal LF}_n$ be a locally free group, and consider its random walk with word length $K$ and drift $l$, the limiting expected normalized word length. Let $T(w)$ be the roof of…

Let ${\cal LF}_n^+$ be the locally free semigroup (the heap) and ${\cal LF}_n$ the locally free group (the colored heap). For a random walk word $w_N$, let $T(w_N)$ denote its roof…

Local-freeness conjecture. Every group $G$ satisfying