7 problems

Aldous–Steele long-range independence conjecture. Some long-range independence property should be helpful in dealing with this difficulty.

Let $F_n$ be a random fullerene, meaning a finite, connected, 3-regular planar graph with faces of degrees both 5 and 6, chosen uniformly from the set of fullerenes with $n$ vertic…

Let $[...$

A sequence of graphs labeled by a spin system has a local weak limit describing the distribution of its finite neighborhoods. Local weak-limit conjecture. Many global properties of…

Let $\mathrm{GIRG}_{W,L}(n)$ denote the finite geometric inhomogeneous random graph with weight distribution $W$ and edge-length distribution $L$, and suppose it satisfies the exte…

Let $G_N$) be finite approximations of a graph $G$, with boundary vertices available as possible roots, and let $r$ be a choice of root on the boundary of $G_N$. Consider the spann…

Limiting-distribution conjecture. $\theta_{d,r,k,t}^{s}$ converges, as $t\to\infty$, to the random $\{0,1\}$-marked tree obtained by assigning independent Bernoulli boundary messag…