Pith Number

pith:LDBPFBV3

pith:2026:LDBPFBV3WIGROCWKGTRQ5UD43J

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Positive-rate PCA and IPS with stationary Bernoulli measures are rapidly forgetful

Ir\`ene Marcovici, Siamak Taati

Probabilistic cellular automata with strictly positive rates and a stationary Bernoulli measure are exponentially ergodic.

arxiv:2605.16904 v1 · 2026-05-16 · math.PR · cond-mat.stat-mech · math-ph · math.MP · nlin.CG

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Claims

C1strongest claim

We prove that every probabilistic cellular automaton with strictly positive transition probabilities that admits a stationary Bernoulli measure is exponentially ergodic. Moreover, the mixing time of any finite region in such a system is logarithmic in the diameter of the region.

C2weakest assumption

The probabilistic cellular automaton admits a stationary Bernoulli measure (the result is conditional on this property, as stated in the abstract).

C3one line summary

Positive-rate probabilistic cellular automata admitting stationary Bernoulli measures are exponentially ergodic with logarithmic mixing times for finite regions.

References

50 extracted · 50 resolved · 0 Pith anchors

[1] Yu. K. Belyaev, Yu. I. Gromak, and V. A. Malyshev. Invariant random Boolean fields.Mathemati- cal Notes of the Academy of Sciences of the USSR, 6(5):792–799, 1969.doi:10.1007/bf01101406 1969 · doi:10.1007/bf01101406

[2] International Journal of Theo- retical Physics 21, 905–940 1982 · doi:10.1007/bf02084158

[3] P. Caputo. Lecture notes on entropy and Markov chains, 2022. URL:http://www.mat.uniroma3. it/users/caputo/ 2022

[4] P. Caputo, Z. Chen, Y. Gu, and Y. Polyanskiy. Entropy contractions in Markov chains: Half- step, full-step and continuous-time.Electronic Journal of Probability, 30, 2025.doi:10.1214/ 25-ejp1372 2025

[5] Locally isoperimetric partitions 2025 · doi:10.1090/tran/

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:03:29.369364Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

58c2f286bbb20d170aca34e30ed07cda4af1f5d29fde344e0187d926dd53cddd

Aliases

arxiv: 2605.16904 · arxiv_version: 2605.16904v1 · doi: 10.48550/arxiv.2605.16904 · pith_short_12: LDBPFBV3WIGR · pith_short_16: LDBPFBV3WIGROCWK · pith_short_8: LDBPFBV3

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/LDBPFBV3WIGROCWKGTRQ5UD43J \
  | 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: 58c2f286bbb20d170aca34e30ed07cda4af1f5d29fde344e0187d926dd53cddd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3957609c4f579a80d90816dd5f66cb2bbae1a2f502619a47125ae7af47c75189",
    "cross_cats_sorted": [
      "cond-mat.stat-mech",
      "math-ph",
      "math.MP",
      "nlin.CG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-05-16T09:30:46Z",
    "title_canon_sha256": "c31c81f9e0fbc36729deba4ad3028e25092f57107b252e0f844e26e8303b7fc9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16904",
    "kind": "arxiv",
    "version": 1
  }
}