Pith Number

pith:4FAJSATU

pith:2026:4FAJSATU6YU2BI7I5MGOH6LAXQ

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Hydrodynamic limits for TASEP with space-time discontinuities

Enrico Scalas, Jacob Butt, Nicos Georgiou

A height-dependent TASEP with space-time discontinuous jump rates has a hydrodynamic limit given by a Lax-Oleinik variational formula for the current.

arxiv:2605.13512 v1 · 2026-05-13 · math.PR

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Claims

C1strongest claim

Combining the law of large numbers for this last-passage model with an extension of the variational coupling method, we prove a hydrodynamic limit for the height function and for the associated particle density.

C2weakest assumption

The speed function is allowed to have discontinuities along locally finitely many curves; the proof relies on this local finiteness to control the variational coupling and the envelope formulation at jumps.

C3one line summary

The height function of TASEP with space-time discontinuous speed function converges to a deterministic limit given by a Lax-Oleinik variational formula that satisfies a discontinuous Hamilton-Jacobi equation.

References

69 extracted · 69 resolved · 1 Pith anchors

[1] Adimurthi and G. D. Veerappa Gowda,Conservation law with discontinuous flux, J. Math. Kyoto Univ.43(2003), no. 1, 27–70. doi:10.1215/kjm/1250283740 2003 · doi:10.1215/kjm/1250283740

[2] D. Aldous and P. Diaconis. Hammersley’s interacting particle process and longest increasing subsequences.Probability Theory and Related Fields, 103:199–213, 1995. doi:10.1007/BF01204214 1995 · doi:10.1007/bf01204214

[3] G. Amir, C. Bahadoran, O. Busani, and E. Saada. Invariant measures for multilane exclusion process.Annales de l’Institut Henri Poincar´ e, Probabilit´ es et Statistiques, 61(3):2184–2234, 2025. doi:10 2025 · doi:10.1214/24-aihp1482

[4] G. Amir, C. Bahadoran, O. Busani, and E. Saada. Hydrodynamics and relaxation limit for multilane exclusion process and related hyperbolic systems.arXiv preprint, arXiv:2501.19355, 2025 2025

[5] Archive for Rational Mechanics and Analysis , author = 2011 · doi:10.1007/s00205-010-0389-4

Receipt and verification

First computed	2026-05-18T02:44:24.545685Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e140990274f629a0a3e8eb0ce3f960bc2c222796f5cf320b6b95df489ba03ab8

Aliases

arxiv: 2605.13512 · arxiv_version: 2605.13512v1 · doi: 10.48550/arxiv.2605.13512 · pith_short_12: 4FAJSATU6YU2 · pith_short_16: 4FAJSATU6YU2BI7I · pith_short_8: 4FAJSATU

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/4FAJSATU6YU2BI7I5MGOH6LAXQ \
  | 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: e140990274f629a0a3e8eb0ce3f960bc2c222796f5cf320b6b95df489ba03ab8

Canonical record JSON

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    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-05-13T13:31:46Z",
    "title_canon_sha256": "9f445496faff74fca8fdc8d48214be24e728b4bcfda8ad66ae6cda4825d44ed4"
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