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Edwards-Wilkinson fluctuations for the directed polymer in the full $L^2$-regime for dimensions $d \geq 3$
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Zygouras, Nikos and Lygkonis, Dimitris (2022) Edwards-Wilkinson fluctuations for the directed polymer in the full $L^2$-regime for dimensions $d \geq 3$. Annales Institut Henri Poincare (B) Probabilites et Statistiques, 58 (1). pp. 65-104. doi:10.1214/21-AIHP1173 ISSN 2308-5827.
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WRAP-Edwards-Wilkinson-fluctuations-directed-polymer-Zygouras-2021.pdf - Accepted Version - Requires a PDF viewer. Download (1301Kb) | Preview |
Official URL: https://doi.org/10.1214/21-AIHP1173
Abstract
We prove that in the full $L^2$-regime the partition function of the directed polymer model in dimensions $d\geq 3$, if centered, {scaled} and averaged with respect to a test function $\varphi \in C_c(\R^d)$, converges in distribution to a Gaussian random variable with explicit variance. Introducing a new idea in this context of a martingale difference representation, we also prove that the log-partition function, which can be viewed as a discretisation of the KPZ equation, exhibits the same fluctuations, when centered and averaged with respect to a test function. Thus, the two models fall within the Edwards-Wilkinson universality class in the full $L^2$-regime, a result that was only established, so far, for a strict subset of this regime in $d\geq 3$.
| 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 | |||||||||
| Library of Congress Subject Headings (LCSH): | Probabilities, Polymers -- Statistical methods, Stochastic processes, Statistical mechanics, Random walks (Mathematics) | |||||||||
| Journal or Publication Title: | Annales Institut Henri Poincare (B) Probabilites et Statistiques | |||||||||
| Publisher: | Institute of Mathematical Statistics | |||||||||
| ISSN: | 2308-5827 | |||||||||
| Official Date: | February 2022 | |||||||||
| Dates: |
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| Volume: | 58 | |||||||||
| Number: | 1 | |||||||||
| Page Range: | pp. 65-104 | |||||||||
| DOI: | 10.1214/21-AIHP1173 | |||||||||
| Status: | Peer Reviewed | |||||||||
| Publication Status: | Published | |||||||||
| Reuse Statement (publisher, data, author rights): | Copyright © 2021 Institute of Mathematical Statistics | |||||||||
| Access rights to Published version: | Restricted or Subscription Access | |||||||||
| Date of first compliant deposit: | 9 August 2021 | |||||||||
| Date of first compliant Open Access: | 9 August 2021 | |||||||||
| RIOXX Funder/Project Grant: |
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