Pith. sign in

REVIEW 1 cited by

Facets of high-dimensional Gaussian polytopes

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

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

arxiv 1808.01431 v2 pith:A4M27NTC submitted 2018-08-04 math.PR

Karoly J Boroczky , Gabor Lugosi , Matthias Reitzner This is my paper · ORCID
classification math.PR
keywords facetsasymptoticgaussiannumberwhenallowedcloseconvex
verification ladder T0 review T1 audit T2 compute T3 formal

Signed reviews

No signed human review yet.

0 comments
read the original abstract

We study the number of facets of the convex hull of n independent standard Gaussian points in d-dimensional Euclidean space. In particular, we are interested in the expected number of facets when the dimension is allowed to grow with the sample size. We establish an explicit asymptotic formula that is valid whenever d/n tends to zero. We also obtain the asymptotic value when d is close to n.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Facets of spherical random polytopes

    math.PR 2019-08 accept novelty 6.0 of 10

    The expected number of facets and the typical facet height of the convex hull of n uniform points on S^{d-1} are determined asymptotically in every regime where n and d tend to infinity.

Pith tools