Pith Number

pith:7YN4NAHC

pith:2026:7YN4NAHC2TQSU3S73VUTRDDFG2

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Percolation representations of additive particle systems

Jan M. Swart

Additive interacting particle systems with finite distributive lattice state spaces admit percolation representations via open paths.

arxiv:2605.13371 v1 · 2026-05-13 · math.PR

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\pithnumber{7YN4NAHC2TQSU3S73VUTRDDFG2}

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Claims

C1strongest claim

It is shown how such a percolation representation can be constructed more generally when the local state space is a finite distributive lattice.

C2weakest assumption

The interacting particle system must be additive and the local state space must be a finite distributive lattice.

C3one line summary

A percolation representation is constructed for additive particle systems with finite distributive lattice state spaces, demonstrated on Krone's two-stage contact process.

References

6 extracted · 6 resolved · 0 Pith anchors

[1] E. Foxall. Duality and complete convergence for multi-type additive growth models. Adv.\ Appl.\ Probab. 48(1) (2016), 32--51 2016

[2] D. Griffeath. Additive and Cancellative Interacting Particle Systems. Lecture Notes in Math. 724, Springer, Berlin, 1979 1979

[3] T.E. Harris. Additive set-valued Markov processes and graphical methods. Ann.\ Probab. 6 (1978), 355--378 1978

[4] S. Krone. The two-stage contact process. Ann.\ Appl.\ Probab. 9(2) (1999), 331--351 1999

[5] A. Sturm and J.M. Swart. Pathwise duals of monotone and additive Markov processes. J.\ Theor.\ Probab. 31(2) (2018), 932--983 2018

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T02:44:47.969426Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fe1bc680e2d4e12a6e5fdd69388c6536b64f5175b523b28eee2b5f16554f6355

Aliases

arxiv: 2605.13371 · arxiv_version: 2605.13371v1 · doi: 10.48550/arxiv.2605.13371 · pith_short_12: 7YN4NAHC2TQS · pith_short_16: 7YN4NAHC2TQSU3S7 · pith_short_8: 7YN4NAHC

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/7YN4NAHC2TQSU3S73VUTRDDFG2 \
  | 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: fe1bc680e2d4e12a6e5fdd69388c6536b64f5175b523b28eee2b5f16554f6355

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "de05c037379e63bae242f71c6d9b6404d30138bfa0302d25e44607abbb928bd0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-05-13T11:28:54Z",
    "title_canon_sha256": "86a2eb04be08111391b9936df8303e2a067f05d137a9c048abaccb1b87433043"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13371",
    "kind": "arxiv",
    "version": 1
  }
}