2 problems

Subcritical phase conjecture. Then $\lambda_\mathsf{c}(\mathscr{G})=\lambda_\mathsf{c}>0$ $\mathbf{P}$-almost surely, and the contact process on $\mathscr{G}$ has a subcritical pha…

Let a kernel-based spatial random graph (KSRG) be a spatial random graph in the class considered in the source, and let ${\mathcal C}(0)$ denote the component of the origin, while…