2 problems

Let $m$ be a positive integer, let $\boldsymbol{p}_m\in(0,1)^m$ have non-increasing entries, and let $\gamma$ be the product parameter used for the cyclic birth and death chain. Fo…

Consider biased random walk on the infinite cluster of supercritical Bernoulli bond percolation on $\mathbb{Z}^d$, and let $\lambda=\lambda_{\mathrm{c}}$ be the critical bias. Let…