Pith Number

pith:YWQZ4FAZ

pith:2026:YWQZ4FAZBH3ZVWFT6ELMDFKB4Q

not attested not anchored not stored refs pending

Randomized quasi-Monte Carlo for walk on spheres

Art B. Owen, Valerie N. P. Ho

Randomized quasi-Monte Carlo in walk-on-spheres yields variance decay slightly better than Monte Carlo for Dirichlet problems.

arxiv:2605.08483 v2 · 2026-05-08 · math.NA · cs.NA · stat.CO

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\usepackage{pith}
\pithnumber{YWQZ4FAZBH3ZVWFT6ELMDFKB4Q}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

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

The median variance rate in 4 RQMC methods over 5 worked examples was slightly better than O(n^{-1.1}). The variance reduction factors ranged from 1.8 to 10.7 at n=2^{17}.

C2weakest assumption

The integrands are periodic indicator functions over regions Θ in the torus T^k whose boundaries have (k-1)-dimensional Minkowski content, allowing application of He and Wang (2015) results.

C3one line summary

Randomized quasi-Monte Carlo applied to walk-on-spheres yields variance reduction factors between 1.8 and 10.7 and median convergence slightly better than O(n^{-1.1}) across five examples.

Cited by

1 paper in Pith

Walk on spheres and Array-RQMC

Receipt and verification

First computed	2026-07-03T00:16:54.040780Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c5a19e141909f79ad8b3f116c19541e42b5da678d26260802d5bd18582df2ad2

Aliases

arxiv: 2605.08483 · arxiv_version: 2605.08483v2 · doi: 10.48550/arxiv.2605.08483 · pith_short_12: YWQZ4FAZBH3Z · pith_short_16: YWQZ4FAZBH3ZVWFT · pith_short_8: YWQZ4FAZ

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/YWQZ4FAZBH3ZVWFT6ELMDFKB4Q \
  | 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: c5a19e141909f79ad8b3f116c19541e42b5da678d26260802d5bd18582df2ad2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5892a826874b41452f3d0968bdb9e2b5133c3fb21a492650afc6f9cee194254f",
    "cross_cats_sorted": [
      "cs.NA",
      "stat.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-05-08T21:01:03Z",
    "title_canon_sha256": "41414cb5d07f8a65549bf8b75cfb6b798857117eb47aa5c72022bf3daa5773d7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.08483",
    "kind": "arxiv",
    "version": 2
  }
}