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Central limit theorems for the (2+1)-dimensional directed polymer in the weak disorder limit
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Gabriel, Simon (2023) Central limit theorems for the (2+1)-dimensional directed polymer in the weak disorder limit. Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, 59 (4). pp. 1984-2016. doi:10.1214/22-aihp1351 ISSN 0246-0203.
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Official URL: https://doi.org/10.1214/22-aihp1351
Abstract
In this article, we present an invariance principle for the paths of the directed random polymer in space dimension two in the subcritical intermediate disorder regime. More precisely, the distribution of diffusively rescaled polymer paths converges in probability to the law of Brownian motion when taking the weak disorder limit. So far analogous results have only been established for
d
≠
2
. Along the way, we prove a local limit theorem which allows us to factorise the point-to-point partition function of the directed polymer into a product of two point-to-plane partition functions.
Dans cet article, nous présentons un principe d’invariance pour les chemins du polymère aléatoire dirigé dans l’espace de dimension deux et dans le régime de désordre intermédiaire sous-critique. Plus précisément, la distribution des chemins de polymères sous un changement d’échelle diffusif converge en probabilité vers la loi du mouvement brownien en prenant la limite de désordre faible. Jusqu’à présent, des résultats analogues n’ont été établis que pour d≠2. En cours de route, nous prouvons un théorème limite local qui nous permet de factoriser la fonction de partition point à point du polymère dirigé en un produit de deux fonctions de partition point à plan.
Item Type: | Journal Article | ||||||
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Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
SWORD Depositor: | Library Publications Router | ||||||
Library of Congress Subject Headings (LCSH): | Statistical mechanics, Polymers, Limit theorems (Probability theory), Symmetry (Physics), Central limit theorem | ||||||
Journal or Publication Title: | Annales de l'Institut Henri Poincaré, Probabilités et Statistiques | ||||||
Publisher: | Institute of Mathematical Statistics | ||||||
ISSN: | 0246-0203 | ||||||
Official Date: | 1 November 2023 | ||||||
Dates: |
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Volume: | 59 | ||||||
Number: | 4 | ||||||
Page Range: | pp. 1984-2016 | ||||||
DOI: | 10.1214/22-aihp1351 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Re-use Statement: | ** From Crossref journal articles via Jisc Publications Router ** History: ppub 01-11-2023; issued 01-11-2023. | ||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||
Date of first compliant deposit: | 30 November 2023 | ||||||
Date of first compliant Open Access: | 1 December 2023 | ||||||
RIOXX Funder/Project Grant: |
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