4 problems

Let ${P}^0$ be the annealed law of an i.i.d. random walk in random environment on $\mathbb Z^d$, and let $S^{d-1}$ be the set of unit vectors in $\mathbb R^d$. For…

Let ${P}^0$ be the annealed law of an i.i.d. random walk in random environment on $\mathbb Z^d$. For $\ell\in S^{d-1}$, let $A_\ell^0$ be the event that…

Let ${P}^0$ be the annealed law of an i.i.d. random walk in random environment on $\mathbb Z^d$. For $\ell\in S^{d-1}$, let $A_\ell^0$ be the event that…

Sznitman's positive-speed conjecture. Any such random walk should have positive speed.