Pith Number

pith:OLCEGV2K

pith:2026:OLCEGV2KOBFU4BNZRZHYVECXML

not attested not anchored not stored refs resolved

Nonconcentration of hitting times for random walks on graphs

Rafael Chiclana

Hitting times of random walks on graphs have variance at least the square of their mean divided by one plus the log of the number of vertices.

arxiv:2605.17513 v1 · 2026-05-17 · math.PR

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\usepackage{pith}
\pithnumber{OLCEGV2KOBFU4BNZRZHYVECXML}

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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

For every connected graph with n vertices, Var_x(τ_y) + E_x τ_y ≥ (E_x τ_y)^2 / (1 + log n), with the logarithmic term sharp up to constants; under bounded degree the additive term can be removed.

C2weakest assumption

The random walk is the simple symmetric random walk on an undirected connected finite graph; the constructions rely on specific high-degree vertex placements that keep variance bounded while making mean linear.

C3one line summary

Establishes variance lower bounds for hitting times of random walks on graphs and disproves a conjecture on local nonconcentration via high-degree constructions.

References

54 extracted · 54 resolved · 0 Pith anchors

[1] Random walks on the random graph , JOURNAL = 2018 · doi:10.1214/17-aop1189

[2] Lubetzky, Eyal and Sly, Allan , TITLE =. Duke Math. J. , FJOURNAL =. 2010 , NUMBER =. doi:10.1215/00127094-2010-029 , URL = 2010 · doi:10.1215/00127094-2010-029

[3] arXiv preprint arXiv:2012.11484 , year= 2012

[4] and Peres, Yuval , TITLE = 2017 · doi:10.1090/mbk/107

[5] Chen, Guan-Yu and Saloff-Coste, Laurent , TITLE =. J. Appl. Probab. , FJOURNAL =. 2013 , NUMBER =. doi:10.1239/jap/1389370092 , URL = 2013 · doi:10.1239/jap/1389370092

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:04:43.164463Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

72c443574a704b4e05b98e4f8a905762e891b11a9a107c2b76b67bcc98037157

Aliases

arxiv: 2605.17513 · arxiv_version: 2605.17513v1 · doi: 10.48550/arxiv.2605.17513 · pith_short_12: OLCEGV2KOBFU · pith_short_16: OLCEGV2KOBFU4BNZ · pith_short_8: OLCEGV2K

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/OLCEGV2KOBFU4BNZRZHYVECXML \
  | 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: 72c443574a704b4e05b98e4f8a905762e891b11a9a107c2b76b67bcc98037157

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6178b6e1ecb9676f21875bbe2e5b79aedbaa26be71ebc8f59853defaee686371",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-05-17T15:57:39Z",
    "title_canon_sha256": "1d6b6267c1192ccb8299e38ed40795829ea6d55716b68eaf66c5f604f61adea4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.17513",
    "kind": "arxiv",
    "version": 1
  }
}