8 problems

Let $(\mathcal{T}_n)_{n\in\mathbb{N}}$ be stationary random tessellations in $\mathbb{R}^d$ converging to a stationary random tessellation $\mathcal{T}$, and let…

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…

Three-dimensional Gibbsian tessellation conjecture. If the rate $\hat f$ satisfies a system of kinetic equations analogous to (1.21), then the outlined strategy should yield a cons…

Setting 1.2 invariance claim. Under Setting 1.2, the law of $(x_1,x_2)\mapsto \rho(x_1,x_2,t)$ is given by

Consider an arrangement of a growing number of random lines in $\mathbb{R}^2$, and let the vertex set be the set of all pairwise intersection points of the lines. Let $f_0$ denote…

Gaussian tessellation embedding conjecture. For random homogeneous Gaussian tessellations of $T$, the condition

Let $\eta$ be a stationary max-stable random field, and let $C(0)$ denote its cell containing the origin. The field is strongly $\beta$-mixing if for every compact set…

Let $K\subseteq S^{n-1}$, let $m(K,\delta)$ be the smallest number of hyperplanes that provide a $\delta$-uniform tessellation of $K$, and let $w(K)$ denote the mean width of $K$.…