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√logt-Superdiffusivity for a Brownian particle in the curl of the 2D GFF
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Cannizzaro, Giuseppe, Haunschmid-Sibitz, Levi and Toninelli, Fabio (2022) √logt-Superdiffusivity for a Brownian particle in the curl of the 2D GFF. The Annals of Probability, 50 (6). pp. 2475-2498. doi:10.1214/22-aop1589 ISSN 0091-1798.
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Official URL: https://doi.org/10.1214/22-aop1589
Abstract
The present work is devoted to the study of the large time behaviour of a critical Brownian diffusion in two dimensions, whose drift is divergence-free, ergodic and given by the curl of the 2-dimensional Gaussian free field. We prove the conjecture, made in (J. Stat. Phys. 147 (2012) 113–131), according to which the diffusion coefficient D(t) diverges as √logt for t→∞. Starting from the fundamental work by Alder and Wainwright (Phys. Rev. Lett. 18 (1967) 988–990), logarithmically superdiffusive behaviour has been predicted to occur for a wide variety of out-of-equilibrium systems in the critical spatial dimension d=2. Examples include the diffusion of a tracer particle in a fluid, self-repelling polymers and random walks, Brownian particles in divergence-free random environments and, more recently, the 2-dimensional critical Anisotropic KPZ equation. Even if in all of these cases it is expected that D(t)∼√logt, to the best of the authors’ knowledge, this is the first instance in which such precise asymptotics is rigorously established.
Item Type: | Journal Article | ||||||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||||||||
SWORD Depositor: | Library Publications Router | ||||||||||||
Library of Congress Subject Headings (LCSH): | Stochastic differential equations, Critical phenomena (Physics), Statistical mechanics | ||||||||||||
Journal or Publication Title: | The Annals of Probability | ||||||||||||
Publisher: | Institute of Mathematical Statistics | ||||||||||||
ISSN: | 0091-1798 | ||||||||||||
Official Date: | 1 November 2022 | ||||||||||||
Dates: |
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Volume: | 50 | ||||||||||||
Number: | 6 | ||||||||||||
Page Range: | pp. 2475-2498 | ||||||||||||
DOI: | 10.1214/22-aop1589 | ||||||||||||
Status: | Peer Reviewed | ||||||||||||
Publication Status: | Published | ||||||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||||||
Copyright Holders: | Copyright © 2022 Institute of Mathematical Statistics | ||||||||||||
Date of first compliant deposit: | 23 November 2023 | ||||||||||||
Date of first compliant Open Access: | 23 November 2023 | ||||||||||||
RIOXX Funder/Project Grant: |
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