REVIEW 1 cited by
Interaction of Poisson hyperplane processes and convex bodies
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Signed reviews
abstract
Given a stationary and isotropic Poisson hyperplane process and a convex body $K$ in ${\mathbb R}^d$, we consider the random polytope defined by the intersection of all closed halfspaces containing $K$ that are bounded by hyperplanes of the process not intersecting $K$. We investigate how well the expected mean width of this random polytope approximates the mean width of $K$ if the intensity of the hyperplane process tends to infinity.
Forward citations
Cited by 1 Pith paper
-
Poisson hyperplane processes and approximation of convex bodies
For Poisson hyperplane K-cells, the expected mean width excess is between n^{-1} log^{d-1} n and n^{-2/(d+1)}, with exact limits for smooth bodies and simplicial polytopes.
Discussion (0). Continue with ORCID to comment.