SDEs with supercritical distributional drifts
Z Hao, X Zhang - arXiv preprint arXiv:2312.11145, 2023 - arxiv.org
Let $ d\geq 2$. In this paper, we investigate the following stochastic differential equation
(SDE) in ${\mathbb R}^ d $ driven by Brownian motion $${\rm d} X_t= b (t, X_t){\rm d} t+\sqrt …
(SDE) in ${\mathbb R}^ d $ driven by Brownian motion $${\rm d} X_t= b (t, X_t){\rm d} t+\sqrt …
Some recent progress on the periodic KPZ equation
Y Gu, T Komorowski - arXiv preprint arXiv:2408.14174, 2024 - arxiv.org
We review recent progress on the study of the Kardar-Parisi-Zhang (KPZ) equation in a
periodic setting, which describes the random growth of an interface in a cylindrical geometry …
periodic setting, which describes the random growth of an interface in a cylindrical geometry …
Weak well-posedness of energy solutions to singular SDEs with supercritical distributional drift
L Gräfner, N Perkowski - arXiv preprint arXiv:2407.09046, 2024 - arxiv.org
We study stochastic differential equations with additive noise and distributional drift on
$\mathbb {T}^ d $ or $\mathbb {R}^ d $ and $ d\geqslant 2$. We work in a scaling …
$\mathbb {T}^ d $ or $\mathbb {R}^ d $ and $ d\geqslant 2$. We work in a scaling …
Superdiffusive central limit theorem for a Brownian particle in a critically-correlated incompressible random drift
We consider the long-time behavior of a diffusion process on $\mathbb {R}^ d $ advected by
a stationary random vector field which is assumed to be divergence-free, dihedrally …
a stationary random vector field which is assumed to be divergence-free, dihedrally …
Effective diffusivities in periodic KPZ
Y Gu, T Komorowski - Probability Theory and Related Fields, 2024 - Springer
For the KPZ equation on a torus with a 1+ 1 spacetime white noise, it was shown in Dunlap
et al.(Commun Pure Appl Math, 2023, https://doi. org/10.1002/cpa. 22110) and Gu and …
et al.(Commun Pure Appl Math, 2023, https://doi. org/10.1002/cpa. 22110) and Gu and …
The Gaussian free-field as a stream function: continuum version of the scale-by-scale homogenization result
P Morfe, F Otto, C Wagner - arXiv preprint arXiv:2404.00709, 2024 - arxiv.org
This note is about a drift-diffusion process $ X $ with a time-independent, divergence-free
drift $ b $, where $ b $ is a smooth Gaussian field that decorrelates over large scales. In two …
drift $ b $, where $ b $ is a smooth Gaussian field that decorrelates over large scales. In two …
Fluctuations of the winding number of a directed polymer on a cylinder
Y Gu, T Komorowski - SIAM Journal on Mathematical Analysis, 2023 - SIAM
Fluctuations of the Winding Number of a Directed Polymer on a Cylinder | SIAM Journal on
Mathematical Analysis Skip to main content logo Brought to you byGoogle Inc Search Search …
Mathematical Analysis Skip to main content logo Brought to you byGoogle Inc Search Search …
A critical drift-diffusion equation: intermittent behavior
F Otto, C Wagner - arXiv preprint arXiv:2404.13641, 2024 - arxiv.org
We consider a drift-diffusion process with a time-independent and divergence-free random
drift that is of white-noise character. We are interested in the critical case of two space …
drift that is of white-noise character. We are interested in the critical case of two space …
Central limit theorem for random walks in divergence free random drift field--revisited
B Tóth - arXiv preprint arXiv:2501.00897, 2025 - arxiv.org
In [Kozma-Toth, Ann. Probab. v 45, pp 4307-4347 (2017)] the weak CLT was established for
random walks in doubly stochastic (or, divergence-free) random environments, under the …
random walks in doubly stochastic (or, divergence-free) random environments, under the …
A Critical Drift-Diffusion Equation: Connections to the Diffusion on
P Morfe, F Otto, C Wagner - arXiv preprint arXiv:2410.15983, 2024 - arxiv.org
In this note, we connect two seemingly unrelated objects: On the one hand is a two-
dimensional drift-diffusion process $ X $ with divergence-free and time-independent drift $ b …
dimensional drift-diffusion process $ X $ with divergence-free and time-independent drift $ b …