Pith Number

pith:WJBSRZQA

pith:2026:WJBSRZQAIDOL2BEC3EWRBIXAFA

not attested not anchored not stored refs resolved

Transport Regimes in Random Walks in Random Environments

Hazel Brookfield, Ian Weatherby, Wei Zhou

Random walks in random environments fall into distinct transport regimes characterized by velocity, diffusivity, and aging.

arxiv:2601.06751 v3 · 2026-01-11 · cond-mat.stat-mech

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications 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

This paper summarizes discrete and continuous time formulations, identifies principal transport regimes through quantitative observables (velocity, diffusivity, mean-square displacement, first-passage, large deviations, aging), and reviews core methods in one dimension (potential/valley mechanisms) and in higher dimensions (environment-seen-from-the-particle, correctors/homogenization, regeneration and ballisticity criteria).

C2weakest assumption

The assumption that the selected literature and observables comprehensively and accurately represent the principal transport regimes without significant omissions in the reviewed body of work.

C3one line summary

The paper summarizes transport regimes in random walks in random environments and reviews core methods in one and higher dimensions.

References

31 extracted · 31 resolved · 3 Pith anchors

[1] S. Havlin and D. Ben-Avraham,Diffusion in disordered media, Adv. Phys.36(1987), 695–798. 10 1987

[2] J.-P. Bouchaud and A. Georges,Anomalous diffusion in disordered media: Statistical mecha- nisms, models and physical applications, Phys. Rep.195(1990), no. 4–5, 127–293 1990

[3] R. Metzler and J. Klafter,The random walk’s guide to anomalous diffusion: A fractional dynamics approach, Phys. Rep.339(2000), no. 1, 1–77 2000

[4] E. W. Montroll and G. H. Weiss,Random walks on lattices. II, J. Math. Phys.6(1965), no. 2, 167–181 1965

[5] Redner,A Guide to First-Passage Processes, Cambridge Univ 2001

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T03:09:32.150400Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b24328e60040dcbd0482d92d10a2e0283003e3723716b1660bcd3acea72d1bb9

Aliases

arxiv: 2601.06751 · arxiv_version: 2601.06751v3 · doi: 10.48550/arxiv.2601.06751 · pith_short_12: WJBSRZQAIDOL · pith_short_16: WJBSRZQAIDOL2BEC · pith_short_8: WJBSRZQA

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/WJBSRZQAIDOL2BEC3EWRBIXAFA \
  | 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: b24328e60040dcbd0482d92d10a2e0283003e3723716b1660bcd3acea72d1bb9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e69ed2b6c3cb7b16306c98367e77d26846b688a341f71949de6a2c2328fbcdbc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cond-mat.stat-mech",
    "submitted_at": "2026-01-11T02:32:26Z",
    "title_canon_sha256": "1981bf470ce41205b315a9b9605ebe450b7241c93f94aa30ea0733a434c1c4d1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2601.06751",
    "kind": "arxiv",
    "version": 3
  }
}