5 problems

Let $G_n$ be a sequence of finite 3-regular graphs with growing girth, converging locally to the 3-regular tree $T_3$, and assume that the thresholds $p^{G_n}$ remain bounded away…

Let $\mathcal{H}^k(n,p)$ be the random $k$-uniform hypergraph with edge probability $p$, and let $j$-components denote components under the adjacency notion used in the paper. Writ…

Unique giant component implies weak concentration conjecture. Under the background assumption, the unique giant component property implies the weak concentration property.

Edge-transitive graph conjecture. One can always rescale the edge-weight so that the background assumption holds; after such rescaling, both the weak concentration and unique giant…

Consider the online power-of-choices geometric graph process on $n$ vertices, with radius … Here $c>0$, $f$ is a function from $(0,\infty)$ to $(0,1)$, and w.h.p. means with high p…