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Vanishing-noise asymptotics for Donsker-Varadhan rate functions on the circle — arXiv:2609.30113

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.30113
License (as archived): CC0-1.0
Archived: 2026-10-08T06:07:58.115Z
SHA-256 of the archived text: 17171e38aa13bede721d2b242d2eb0c83eea1fa2ea2ebd482bc4762d75174808
Stable URL of this page: https://metraipolis.com/documento/dc_cdc84bee18af

How to cite

Vanishing-noise asymptotics for Donsker-Varadhan rate functions on the circle — arXiv:2609.30113 — arXiv (en), https://arxiv.org/abs/2609.30113 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_cdc84bee18af (Metraipolis archive dc_cdc84bee18af, sha256 17171e38aa13bede721d2b242d2eb0c83eea1fa2ea2ebd482bc4762d75174808)

BibTeX

@misc{dccdc84bee18af,
  title = {Vanishing-noise asymptotics for Donsker-Varadhan rate functions on the circle — arXiv:2609.30113},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.30113},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_cdc84bee18af; sha256 17171e38aa13bede721d2b242d2eb0c83eea1fa2ea2ebd482bc4762d75174808},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.30113. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We study the vanishing-noise limit of the rate function for the Donsker-Varadhan large deviation principle for one-dimensional diffusion processes on a circle. As is well known, the rate function can be represented either as the Legendre transform of the principal eigenvalue of the perturbed infinitesimal generator or by a variational formula. We analyze the asymptotic behavior of the principal eigenvalue as the parameter in front of the noise goes to zero and compare the Legendre transform of the limit with the expression obtained as the limit of the variational representation. We prove, in particular, that the resulting expressions do not always coincide, leading to continuity and discontinuity phenomena in infinite-dimensional functional spaces. Moreover, we use the previous analysis to pass to the limit in the LDP, using the notion of {\Gamma}-convergence.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-25 in math.PR).
Categorie arXiv: Probability (math.PR).
Pagina del lavoro: https://arxiv.org/abs/2609.30113 — 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 2026-10-08T05:35:05.155Z dalla pagina https://arxiv.org/catchup/math.PR/2026-09-25?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).