9 problems

Poisson–Voronoi random-walk conjecture. Then there are some $q(s),r_o(s)>0$ such that for all starting points with $|x|\geq r_o(s)$:

Let $\mathcal V_{\text{typ}}$ be the typical cell of a Poisson–Voronoi tessellation in dimension $d$, with intensity $\lambda=\lambda(d)>0$, and let $B$ denote the unit ball in…

Let $E$ be an interval of type (i) or (ii) in the construction of the tessellation $\mathcal{L}_{d,\gamma}(f)$, and let the resulting tessellation be generated by the corresponding…

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 E…

For each dimension $d$, consider Poisson-Voronoi percolation on $d$-dimensional hyperbolic space ${\mathbb H}^d$, with intensity $bb$, and let the typical cell be the typical Poiss…

Let $p_c(bb)$ denote the critical value for Poisson-Voronoi percolation on the hyperbolic plane as a function of the intensity $bb$. Differentiability conjecture. … is differentiab…

Let $p_c(bb)$ denote the critical value for Poisson-Voronoi percolation on the hyperbolic plane as a function of the intensity $bb$. Benjamini–Schramm monotonicity conjecture. … is…

Let $p_c(bb)$ denote the critical value for Poisson-Voronoi percolation on the hyperbolic plane. Small-intensity lower-bound conjecture. There exists a $bb_0>0$ such that … for all…

Let $d\in\mathbb{N}$ and $k\in\{0,\ldots,d-1\}$. Write $\mathcal{V}_d$ for the Poisson–Voronoi polytope in dimension $d$, and let $\mathbb{E}f_k(\mathcal{V}_d)$ denote its expected…