High-dimensional ellipsoids converge to Gaussian spaces

Daisuke Kazukawa; Takashi Shioya

High-dimensional ellipsoids converge to Gaussian spaces

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 2003.05105 v1 pith:Y3JTPIYZ submitted 2020-03-11 math.MG math.DG

Daisuke Kazukawa , Takashi Shioya This is my paper · ORCID

classification math.MGmath.DG

keywords concentrationconvergentellipsoidsgaussianirreduciblenontrivialtopologyconstructed

verification ladder T0 review T1 audit T2 compute T3 formal

0 comments

read the original abstract

We prove the convergence of (solid) ellipsoids to a Gaussian space in Gromov's concentration/weak topology as the dimension diverges to infinity. This gives the first discovered example of an irreducible nontrivial convergent sequence in the concentration topology, where 'irreducible nontrivial' roughly means to be not constructed from Levy families nor box convergent sequences.

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

Poincar\'e Beta Balls: Radial Laws, Shell Transforms, and Phase Diagram
math.MG 2026-07 accept novelty 7.0 of 10

Rescaled Poincaré beta balls converge weakly to one of four pyramids—finite star trees, diameter ≤1, metric-transformed Gaussians, or the Gaussian pyramid—according to the A and βL balance.

Pith tools