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Continuous-time directed polymers to the Critical SHF via moments — arXiv:2608.11603

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.11603
License (as archived): CC0-1.0
Archived: 2026-10-19T05:47:23.628Z
SHA-256 of the archived text: b6e6de28c97dd520c0cca9f227c7241d9f02c392ef73f011c1405f59e4d29feb
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How to cite

Continuous-time directed polymers to the Critical SHF via moments — arXiv:2608.11603 — arXiv (en), https://arxiv.org/abs/2608.11603 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_cd20764a2bd7 (Metraipolis archive dc_cd20764a2bd7, sha256 b6e6de28c97dd520c0cca9f227c7241d9f02c392ef73f011c1405f59e4d29feb)

BibTeX

@misc{dccd20764a2bd7,
  title = {Continuous-time directed polymers to the Critical SHF via moments — arXiv:2608.11603},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.11603},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_cd20764a2bd7; sha256 b6e6de28c97dd520c0cca9f227c7241d9f02c392ef73f011c1405f59e4d29feb},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.11603. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We consider a class of two-dimensional continuous-time directed random polymers in a correlated Brownian environment. The partition functions of these polymers form a discrete approximation of the Critical Stochastic Heat Flow (SHF), constructed by Caravenna, Sun and Zygouras (2023). Using a recent moment based axiomatic characterization of the SHF by Tsai (2024), we prove that the point-to-point partition functions, viewed as random measures, converge to the critical SHF. The proof proceeds by first establishing convergence of all moments through the resolvent method introduced by Gu, Quastel and Tsai (2021) and based on Rajeev (1999) and Dimock and Rajeev (2004). This is followed by establishing tightness and verifying the remaining axioms in the characterization.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-08-13 in math.PR).
Categorie arXiv: Probability (math.PR).
Pagina del lavoro: https://arxiv.org/abs/2608.11603 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-19T05:40:02.419Z dalla pagina https://arxiv.org/catchup/math.PR/2026-08-13?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).