3 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 $\mathcal{Z}$ be the zigzag graph, let $\partial_{M}\mathcal{Z}$ and $\partial_{\min}\mathcal{Z}$ denote its Martin and minimal entrance boundaries, and let $\mathcal{U}^{(2)}$…

Let $(M,\rho)$ be a reversible random planar map. The Martin boundary of $M$ is the boundary describing asymptotic behavior of positive harmonic functions for random walk on $M$. A…