3 problems

Hutchcroft's Erdős–Rényi universality conjecture. This model is in the Erdős–Rényi universality class when

Let $M_n(\beta)$ denote the quantity in Proposition maximumupper, and let the inequality asserted there be the upper bound on $M_n(\beta)$ obtained in that proposition. Maximum-clu…

Let $K$ denote the cluster of the origin in critical long-range percolation on the hierarchical lattice, and let $\beta_c$ be the critical parameter. The exponent $\delta$ is defin…