Pith Number

pith:JFDIEY6W

pith:2026:JFDIEY6WCT4QHEIGR4PYU4SFQK

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Set-indexed and multiple sums in high dimensions

Alexander Marynych, Bochen Jin, Ilya Molchanov

Sets of values from multiple and set-indexed sums of random vectors converge in probability to a generalized Wiener spiral when viewed as metric spaces in growing dimensions.

arxiv:2605.15783 v1 · 2026-05-15 · math.PR

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Record completeness

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4 Citations open

5 Replications open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

It is shown that, when viewed as finite metric spaces, the sets of values of such sums converge in probability. The limit is identified as a generalisation of the Wiener spiral, which appears as the high-dimensional limit of single-index sums.

C2weakest assumption

The random vectors are assumed to satisfy conditions that allow the high-dimensional limit to exist and be identified with the generalized Wiener spiral (implicit in the statement that the limit is identified).

C3one line summary

Sets of values of multiple and set-indexed sums of random vectors converge in probability to a generalization of the Wiener spiral as dimension grows.

References

10 extracted · 10 resolved · 1 Pith anchors

[1] Adams and Andrew B 2012

[2] Dmitri Burago, Yuri Burago, and Sergei Ivanov,A course in metric geometry, American Mathematical So- ciety, Providence, RI, 2001. MR 1835418 2001

[3] Bochen Jin,Convergence of random walks inℓ p-spaces of growing dimension, Modern Stochastics: Theory and Applications (2026), 1–11 2026

[4] Ranges of Extremal Processes and Heavy-Tailed Random Walks in Spaces of Growing Dimension 2025 · arXiv:2510.18780

[5] Zakhar Kabluchko and Alexander Marynych,Random walks in the high-dimensional limit I: The Wiener spiral, Ann. Inst. Henri Poincar´e Probab. Stat.60(2024), no. 4, 2945–2974. MR 4828862 2024

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:01:18.049788Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

49468263d614f90391068f1f8a724582ab2967205c2d771b0140ac7f66c48c00

Aliases

arxiv: 2605.15783 · arxiv_version: 2605.15783v1 · doi: 10.48550/arxiv.2605.15783 · pith_short_12: JFDIEY6WCT4Q · pith_short_16: JFDIEY6WCT4QHEIG · pith_short_8: JFDIEY6W

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/JFDIEY6WCT4QHEIGR4PYU4SFQK \
  | 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: 49468263d614f90391068f1f8a724582ab2967205c2d771b0140ac7f66c48c00

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1cd4516c8c909870595071c65b024a96f60a670932de65e62cf2d045c8315305",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-05-15T09:42:26Z",
    "title_canon_sha256": "7121a3d6a987822e3b3a660e2c43494194da4d1c281c99c3ca6f772db7fbb249"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15783",
    "kind": "arxiv",
    "version": 1
  }
}