Pith Number

pith:PGXIV3IW

pith:2026:PGXIV3IWBXEO3JDLFTDMZKWILK

not attested not anchored not stored refs resolved

Loop pruning and downward deviations for maximum local time of discrete-time simple random walks

Xinyi Li, Yushu Zheng

Loop pruning transfers the continuous-time lower bound to prove sharp asymptotics for downward deviations of discrete random walk local times.

arxiv:2605.16086 v1 · 2026-05-15 · math.PR

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\pithnumber{PGXIV3IWBXEO3JDLFTDMZKWILK}

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3 Author claim open · sign in to claim

4 Citations 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

We prove this lower bound and hence obtain the sharp asymptotic formula for the downward-deviation probability.

C2weakest assumption

The loop-pruning decomposition and associated random structure accurately isolate the necessary path properties to transfer the continuous-time lower-bound argument to discrete time without introducing uncontrolled errors (introduced in the present paper to handle the discrete-time case).

C3one line summary

The paper establishes the lower bound for the downward-deviation probability of the maximum local time of discrete-time simple random walks in d ≥ 3 via a new loop-pruned random walk structure, yielding the sharp asymptotic.

References

14 extracted · 14 resolved · 1 Pith anchors

[1] Stochastic processes and their applications , volume= 2005

[2] Random walk in random and non-random environments , author=. 2013 , publisher= 2013

[3] arXiv preprint arXiv:2409.00995 , year=

[4] Thick points of random walk and the Gaussian free field , author=

[5] Probability Theory and Related Fields , volume= 2013

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:01:52.052882Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

79ae8aed160dc8eda46b2cc6ccaac85a8c829d6d25b95ebc655005d2cf0ee10f

Aliases

arxiv: 2605.16086 · arxiv_version: 2605.16086v1 · doi: 10.48550/arxiv.2605.16086 · pith_short_12: PGXIV3IWBXEO · pith_short_16: PGXIV3IWBXEO3JDL · pith_short_8: PGXIV3IW

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/PGXIV3IWBXEO3JDLFTDMZKWILK \
  | 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: 79ae8aed160dc8eda46b2cc6ccaac85a8c829d6d25b95ebc655005d2cf0ee10f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1dcbafd92e52dce5d01105e38d053d5d79613fcc5fccc3c28894fedc2f3caa8e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-05-15T15:46:45Z",
    "title_canon_sha256": "11963e1b6733517de6141352696bb53841e6c6c65d818d24c58997a8f251cdf4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16086",
    "kind": "arxiv",
    "version": 1
  }
}