Lucas Flammant

A finite-graph conjecture related to $\theta(p_c)=0$ for Bernoulli bond percolation on $\mathbb Z^d$

We introduce a conjecture for Bernoulli bond percolation on finite graphs. Roughly speaking, it asserts that if each boundary vertex is associated with a highly probable event that is increasing with respect to the percolation configuration, then, conditionally on the origin being connected to the boundary, the origin...