2 problems

Let $d\geq 2$ and let $\mathbf{u}\in S^{d-1}$ be a direction. Write $A_{\mathbf{u}}$ for the event of transience in direction $\mathbf{u}$, and let $\tau_{\mathbf{u},1}$ be the fir…

Let $d\geq 2$. Consider a uniformly elliptic, ballistic, nearest-neighbor random walk in random environment, and let the regeneration times be defined in a direction of transience.…