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• W2923747351 abstract "We prove an explicit combinatorial formula for the expected number of faces of the zero polytope of the homogeneous and isotropic Poisson hyperplane tessellation in $mathbb R^d$. The expected $f$-vector is expressed through the coefficients of the polynomial $$ (1+ (d-1)^2x^2) (1+(d-3)^2 x^2) (1+(d-5)^2 x^2) ldots. $$ Also, we compute explicitly the expected $f$-vector and the expected volume of the spherical convex hull of $n$ random points sampled uniformly and independently from the $d$-dimensional half-sphere. In the case when $n=d+2$, we compute the probability that this spherical convex hull is a spherical simplex, thus solving an analogue of the Sylvester four-point problem on the half-sphere." @default.
• W2923747351 created "2019-04-01" @default.
• W2923747351 creator A5010851411 @default.
• W2923747351 date "2019-01-29" @default.
• W2923747351 modified "2023-09-27" @default.
• W2923747351 title "Expected $f$-vector of the Poisson Zero Polytope and Random Convex Hulls in the Half-Sphere" @default.
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