3 problems

Let $F$ be the limit set of Mandelbrot percolation with subdivision parameter $N\geq 2$ in dimension $d\geq 1$. Let $p_d$ denote the threshold for the dust phase and $p_c$ the crit…

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 $d\geq 2$ and $N\geq 2$. In full-space fractal percolation, let $\hat{p}_c(N,d)$ denote the threshold at which the limiting retained set ceases to be totally disconnected, and…