Pith Number

pith:RIJSCIVU

pith:2026:RIJSCIVUCVW7A5NVMYVP46NDUW

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Non-asymptotic quantisation of spherically symmetric distributions

Anatoly Zhigljavsky, Luc Pronzato

For spherically symmetric distributions, random quantizers placed uniformly on a sphere of optimal radius achieve low expected distortion even with moderate numbers of points in high dimensions.

arxiv:2605.12568 v1 · 2026-05-12 · math.ST · math.PR · stat.ML · stat.TH

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Claims

C1strongest claim

For spherically symmetric distributions, random quantisers uniformly distributed on a sphere of suitable radius r achieve exceptional performance; the expected distortion is a triple integral computable with arbitrary precision, and the optimal r can be determined numerically, with approximations from extreme-value theory when n scales with d.

C2weakest assumption

The distributions under study are spherically symmetric, and the claimed performance advantage holds specifically for moderate n where the asymptotic regime of Zador's theorem has not yet been reached.

C3one line summary

For spherically symmetric distributions, random points on an optimally chosen sphere achieve low expected distortion for moderate n, with radius approximations derived from extreme value theory.

References

13 extracted · 13 resolved · 0 Pith anchors

[1] N. Alon and J.H. Spencer.The Probabilistic Method. Wiley, 2000. Second edition 2000

[2] K.-T. Fang, S. Kotz, and K.W. Ng.Symmetric Multivariate and Related Dis- tributions. Chapman and Hall/CRC, 1990 1990

[3] Feller.An Introduction to Probability Theory and Its Applications, vol 1971

[4] S. Graf and H. Luschgy.Foundations of Quantization for Probability Distribu- tions. Springer, Berlin, 2000 2000

[5] S. Kotz and S. Nadarajah.Extreme Value Distributions: Theory and Applica- tions. Imperial College Press, 2000 2000

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T03:10:01.812477Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8a132122b4156df075b5662afe79a3a5abf08abbbbe817946a10b1b0647c761b

Aliases

arxiv: 2605.12568 · arxiv_version: 2605.12568v1 · doi: 10.48550/arxiv.2605.12568 · pith_short_12: RIJSCIVUCVW7 · pith_short_16: RIJSCIVUCVW7A5NV · pith_short_8: RIJSCIVU

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/RIJSCIVUCVW7A5NVMYVP46NDUW \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 8a132122b4156df075b5662afe79a3a5abf08abbbbe817946a10b1b0647c761b

Canonical record JSON

{
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    "abstract_canon_sha256": "df5a1c45dbcc0a73016cc3cca4841e21912ba9508e6adc963051479ad20fcc83",
    "cross_cats_sorted": [
      "math.PR",
      "stat.ML",
      "stat.TH"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2026-05-12T10:01:41Z",
    "title_canon_sha256": "0d81d3efbd7228f23ec73de7b30a7f983a435bb24423708560d5f1f2b65aca9c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.12568",
    "kind": "arxiv",
    "version": 1
  }
}