High-intensity Euclidean-limit conjecture for hyperbolic Poisson-Voronoi percolation

For each dimension $d$, let $p_c^{\mathbb H^d}(bb)$ and $p_c^{\mathbb R^d}(bb)$ denote the critical values for Poisson-Voronoi percolation on $d$-dimensional hyperbolic space and Euclidean space, respectively, at intensity $bb$. High-intensity Euclidean-limit conjecture. For every $d$, as the intensity $bb\to\infty$, the critical value for Poisson-Voronoi percolation on ${\mathbb H}^d$ tends to the critical value for Poisson-Voronoi percolation on ${\mathbb R}^d$. The statement is motivated by the authors' separate result that the hyperbolic critical value tends to $1/2$ in the planar case and by the expectation that this result extends to arbitrary dimensions.