3 problems

For loop percolation on the integer lattice $\mathbb{Z}^d$, let $\alpha_c(0)$ denote the critical parameter for percolation at $\kappa=0$, and let … denote the associated susceptib…

Consider a percolation process on a sufficiently regular rhombus tiling, with critical threshold $p_c$ and stable directions associated with the process. Stable-direction critical-…

Let $\omega_p$ be Bernoulli site percolation on $\mathbb{Z}^d$, and let $C^\infty(\omega_p)$ be the set of vertices belonging to infinite open clusters. For a graph obtained by del…