Pith Number

pith:E5RJP5QR

pith:2026:E5RJP5QRGETS6YV6OL3B3PWC4R

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Mixing times of Langevin dynamics for spiked matrix models

Curtis Grant, Reza Gheissari, Tianmin Yu

Langevin dynamics for large-signal spiked matrices mix in O(log N) from uniform spherical starts even below the critical temperature.

arxiv:2604.20008 v2 · 2026-04-21 · math.PR

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\pithnumber{E5RJP5QRGETS6YV6OL3B3PWC4R}

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Claims

C1strongest claim

Initialized from the uniform-at-random spherical prior, the mixing time in the low-temperature α>1 regime is O(log N). The exact exponential rate of the (worst-case initialization) mixing time for low temperatures is given by the difference of the free energies of the spiked and null models.

C2weakest assumption

The analysis is performed in the regime where the signal-to-noise ratio θ is large but remains order one; the fast-mixing claim requires the initialization to be symmetric with respect to the top eigenvector of the spiked matrix.

C3one line summary

For spiked Wigner matrices, Langevin dynamics mixes in O(log N) time from uniform or top-eigenvector-symmetric starts below the critical inverse temperature 1/θ, while worst-case mixing is exponential in N with rate equal to the free-energy difference between spiked and null models.

Receipt and verification

First computed	2026-05-22T01:03:19.439890Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

276297f61131272f62be72f61dbec2e4462bb03c9f25f11ba514972a5a0c2b8f

Aliases

arxiv: 2604.20008 · arxiv_version: 2604.20008v2 · doi: 10.48550/arxiv.2604.20008 · pith_short_12: E5RJP5QRGETS · pith_short_16: E5RJP5QRGETS6YV6 · pith_short_8: E5RJP5QR

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/E5RJP5QRGETS6YV6OL3B3PWC4R \
  | 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: 276297f61131272f62be72f61dbec2e4462bb03c9f25f11ba514972a5a0c2b8f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2bca6b108818af64f79cb883d81cdd030fa961a3a2375037512b44327f065c0b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-04-21T21:36:21Z",
    "title_canon_sha256": "1c62f13a961f7791cf3fe415085b048004827c02a7462c175fbb514a422fdf53"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.20008",
    "kind": "arxiv",
    "version": 2
  }
}