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- W3166771936 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. Toth, B. Valko, J. Stat. Phys., 2012], according to which the diffusion coefficient $D(t)$ diverges as $sqrt{log t}$ for $ttoinfty$. Starting from the fundamental work by Alder and Wainwright [B. Alder, T. Wainright, 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 $D(t)simsqrt{log t}$, to the best of the authors' knowledge, this is the first instance in which such precise asymptotics is rigorously established." @default.
- W3166771936 created "2021-06-22" @default.
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- W3166771936 date "2022-01-31" @default.
- W3166771936 modified "2023-09-26" @default.
- W3166771936 title "$sqrt{log t}$-superdiffusivity for a Brownian particle in the curl of the 2d GFF" @default.
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