3 problems

Let $\mathcal C$ be the set of cutpoints of the random walk, and let $\alpha$ be a real number. Under the conditions of Theorem, fractional-moment conjecture. … for all $\alpha<1$.…

Benjamini–Gurel-Gurevich–Schramm conjecture. The path graph $\operatorname{PATH}$ has almost surely infinitely many cutpoints.

Let $\{X_n\}$ be the transient nearest-neighbor random walk described above, and call a site a cutpoint or a strong cutpoint according to the definitions in the paper. A strong cut…