6 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:

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

Exponential-relaxation conjecture. If there exists $\kappa>0$ such that

Let ${\mathcal U}$ be a critical update family with an infinite number of stable directions. Let $q$ denote the vacancy probability, let $\tau_0$ be the infection time at the origi…

Let $\tau_{0}$ be the relaxation time at the origin in the mixed threshold FA model, let $q$ be the vacancy density, let $\nu$ denote the law of the random environment, and let…

Let ${\mathcal U}$ be an $\alpha$-unrooted and unbalanced critical two-dimensional update family with difficulty $\alpha$. Let $q$ denote the vacancy density and let $\tau_0$ be th…