3 problems

Let ${\bf X}^0(t)$ be the East process on the positive integers, started from a single particle at site $0$. Let $r({\bf x})$ be the rightmost occupied site in configuration…

Stationary-measure decomposition conjecture. If $\mu$ is a stationary measure of a KCM, then there exists a probability measure $\mu_{*}$ on $\mathcal{E}$ such that

Let the environment be the East model at density $1/2$, and let $v(\e)$ denote the asymptotic velocity of the $\e$-random walk. Asymptotic velocity conjecture. For $\e>0$ (respecti…