6 problems

Invasion percolation scaling conjecture. For each $r\geq2$, $\vec t\in\mathbb{R}^{r-1}$ and $\vec k\in\mathbb{R}^{d(r-1)}$, there exist constants $A,V,v$ and $\delta\in(0,1)$ such…

Invasion percolation one-point function conjecture.

Let the invasion percolation cluster be the infinite cluster produced by the invasion percolation process, and let the IIC denote the incipient infinite cluster, namely the critica…

Let $T(\clock)$ be the branching process tree, and let … be the $k$-neighbourhood of the invasion percolation cluster. Under the conditions of the volume-growth theorem, let…

Write $\mathrm{K}_n=([n],{[n] \choose 2},\mathrm{U})$ for the randomly weighted complete graph, and let $F(\mathrm{K}_n,[k(n)])$ be the invasion-percolation forest started from…

Universality conjecture. FPP on the complete graph is in the same universality class as IP.