Pith Number

pith:YEMWLOBP

pith:2026:YEMWLOBPEWUPY3PERCVMYBSNTQ

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Walk on spheres and Array-RQMC

Art B. Owen, Valerie N. P. Ho

Array-RQMC sampling in the walk on spheres algorithm reduces Monte Carlo variance by factors of 57 to 2290 at sample size 2 to the 17.

arxiv:2605.12844 v1 · 2026-05-13 · math.NA · cs.NA · stat.CO

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3 Author claim open · sign in to claim

4 Citations open

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Claims

C1strongest claim

Array-RQMC-WOS reduces the Monte Carlo variance by factors ranging from 57-fold to 2290-fold at n=2^{17} trajectories, attaining empirical rates between n^{-1.4} and n^{-1.8}.

C2weakest assumption

That the observed variance reductions and higher column-wise mean dimension will persist for problems outside the tested collection and that the Sobol'-index-based mean dimension correctly isolates the source of the improvement.

C3one line summary

Array-RQMC-WOS cuts Monte Carlo variance by 57-2290 times with empirical rates n^{-1.4} to n^{-1.8} and introduces a column-wise mean dimension to explain the gain.

References

45 extracted · 45 resolved · 1 Pith anchors

[1] Bilyk, D., V. N. Temlyakov, and R. Yu (2012). Fibonacci sets and symmetrization in discrepancy theory. Journal of Complexity\/ 28\/ (1), 18--36 2012

[2] Binder, I. and M. Braverman (2012). The rate of convergence of the walk on spheres algorithm. Geometric and Functional Analysis\/ 22\/ (3), 558--587 2012

[3] Caflisch, R. E., W. Morokoff, and A. B. Owen (1997). Valuation of mortgage backed securities using Brownian bridges to reduce effective dimension. Journal of Computational Finance\/ 1 , 27--46 1997

[4] Choi, S.-C. T., F. J. Hickernell, M. McCourt, J. Rathinavel, and A. G. Sorokin (2026). QMCPy : A Q uasi- M onte C arlo P ython L ibrary 2026

[5] Cools, R., F. Y. Kuo, and D. Nuyens (2006). Constructing embedded lattice rules for multivariate integration. SIAM Journal on Scientific Computing\/ 28\/ (6), 2162--2188 2006

Receipt and verification

First computed	2026-05-18T03:09:11.920332Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c11965b82f25a8fc6de488aacc064d9c06c6ca39892e0e923889c4680f3baacc

Aliases

arxiv: 2605.12844 · arxiv_version: 2605.12844v1 · doi: 10.48550/arxiv.2605.12844 · pith_short_12: YEMWLOBPEWUP · pith_short_16: YEMWLOBPEWUPY3PE · pith_short_8: YEMWLOBP

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/YEMWLOBPEWUPY3PERCVMYBSNTQ \
  | 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: c11965b82f25a8fc6de488aacc064d9c06c6ca39892e0e923889c4680f3baacc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cdbb9d8a0d174b7ed185ec058d9b3834d9dd2cb9f7533b397b7ac421b9280066",
    "cross_cats_sorted": [
      "cs.NA",
      "stat.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-05-13T00:42:15Z",
    "title_canon_sha256": "85fd35ed3054fb888248818f445ff01eb266b21763aa01ae6ab6db8432278e37"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.12844",
    "kind": "arxiv",
    "version": 1
  }
}