2 problems

Large-deviation conjecture for the typical Poisson zero-cell vertex number
Let $\mathcal Z_d^{\text{typ}}$ denote the typical Poisson zero cell, and let $f_0(\mathcal Z_d^{\text{typ}})$ be its number of vertices. Large-deviation conjecture. As…
openFrom paperslarge-deviations poisson-polyhedra random-polytopes
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7
Poisson zero-cell face-probability limit conjecture
Fix $k\in\{2,3,\ldots\}$ and sample $k$ vertices uniformly at random from the vertices of the random polytope $\operatorname{conv}\Pi_{d,1}$ . Let…
openFrom papersasymptotic-probability poisson-polyhedra random-polytopes
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6

Large-deviation conjecture for the typical Poisson zero-cell vertex number