3 problems

Aldous's conjecture. As $q\downarrow 0$, the rescaled stationary East process converges to a limit point process $X_t$ on $[0,+\infty)$ such that:

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