Pith Number

pith:IENCCCCZ

pith:2026:IENCCCCZYZ7ZGJHK2TG6ZBQTPS

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Large deviations for maximum local time of simple random walk in dimensions $d\ge 3$

Xinyi Li, Yushu Zheng

Simple random walks in three or more dimensions have sharp large-deviation asymptotics for their maximum local time, along with Gumbel fluctuations.

arxiv:2604.10214 v2 · 2026-04-11 · math.PR

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\pithnumber{IENCCCCZYZ7ZGJHK2TG6ZBQTPS}

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Claims

C1strongest claim

We obtain sharp asymptotic probabilities for upward and downward large deviations of the maximum local time of simple random walks on Z^d, d ≥ 3. We also obtain Gumbel-type fluctuations around the logarithmic scale of the maximum local time.

C2weakest assumption

The results assume the standard simple symmetric random walk on Z^d for d ≥ 3 together with implicit regularity conditions that allow the large-deviation and fluctuation statements to hold.

C3one line summary

Sharp asymptotic probabilities for large deviations of the maximum local time of simple random walks in d ≥ 3, plus Gumbel fluctuations around its logarithmic scale.

Cited by

1 paper in Pith

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

Receipt and verification

First computed	2026-05-26T02:05:09.154347Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

411a210859c67f9324ead4cdec86137cb0b705ce883eb830e6f090ff0c7ba3e2

Aliases

arxiv: 2604.10214 · arxiv_version: 2604.10214v2 · doi: 10.48550/arxiv.2604.10214 · pith_short_12: IENCCCCZYZ7Z · pith_short_16: IENCCCCZYZ7ZGJHK · pith_short_8: IENCCCCZ

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/IENCCCCZYZ7ZGJHK2TG6ZBQTPS \
  | 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: 411a210859c67f9324ead4cdec86137cb0b705ce883eb830e6f090ff0c7ba3e2

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": "2026-04-11T13:46:24Z",
    "title_canon_sha256": "2234d998c2a9a896d7fd523990eba9908a312bf9930396aba952108f43235129"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.10214",
    "kind": "arxiv",
    "version": 2
  }
}