4 problems

Let ${\cal Z}$ be the graded graph of zigzag diagrams, with level-${n}$ vertices ${\cal Z}_n$. For a sequence $(\lambda_n\in{\cal Z}_n)$, let $\iota_n(\lambda_n)$ be its image in t…

Let $G$ be a graded graph with root $\rho$, levels $V_0,\ldots,V_N$, and IID vertex labels with common distribution $\mu$. For an event $B$ of label sequences, let $P(G;B)$ be the…

Let $Y$ be a poset, let $L(Y)$ be the distributive lattice of all finite ideals of $Y$, and let $\Gamma$ be the Hasse diagram of $L(Y)$. Consider the space of all minimal infinite…

Let $\Gamma$ be a graded graph and let $\mu$ be an ergodic central measure on the path space $T(\Gamma)$. Let $\rho=\rho_0$ be a metric on $T(\Gamma)$ such that…