<div class="csl-bib-body">
<div class="csl-entry">Toninelli, F. L. (2025, April 16). <i>sqrt{log t} superdiffusivity for a Brownian particle in the curl of the 2d GFF</i> [Conference Presentation]. Workshop “Regularization by noise,” TU WIEN, Austria.</div>
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/214486
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dc.description
https://regbynoise2025.conf.tuwien.ac.at/
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dc.description.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 [B. Tóth,B. Valkó, J. Stat. Phys., 2012], according to which the diffusion coefficient D(t) diverges as sqrt(log t) for t → ∞.
Starting from the fundamental work by Alder and Wainwright [B. Alder, T. Wainwright, Phys.
Rev. Lett. 1967], 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) ∼ sqrt(log t), this is the first instance in which such precise asymptotics is rigorously established.
en
dc.language.iso
en
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dc.subject
Stochastic differential equations
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dc.subject
superdiffusion
en
dc.title
sqrt{log t} superdiffusivity for a Brownian particle in the curl of the 2d GFF
