Some recent progress on the periodic KPZ equation
Y Gu, T Komorowski - … and Partial Differential Equations: Analysis and …, 2025 - Springer
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 …
Gaussian Fluctuations for the Stochastic Burgers Equation in Dimension
The goal of the present paper is to establish a framework which allows to rigorously
determine the large-scale Gaussian fluctuations for a class of singular SPDEs at and above …
determine the large-scale Gaussian fluctuations for a class of singular SPDEs at and above …
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 …
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 …
The Gaussian free-field as a stream function: asymptotics of effective diffusivity in infra-red cut-off
G Chatzigeorgiou, P Morfe, F Otto, L Wang - arXiv preprint arXiv …, 2022 - arxiv.org
We analyze the large-time asymptotics of a passive tracer with drift equal to the curl of the
Gaussian free field in two dimensions with ultra-violet cut-off at scale unity. We prove that the …
Gaussian free field in two dimensions with ultra-violet cut-off at scale unity. We prove that the …
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 …
Weak coupling limit of the Anisotropic KPZ equation
We study the 2-dimensional anisotropic KPZ equation (AKPZ), which is formally given by∂
th= 1 2 Δ h+ λ ((∂ 1 h) 2−(∂ 2 h) 2)+ ξ, where ξ denotes a space-time white noise and λ> 0 …
th= 1 2 Δ h+ λ ((∂ 1 h) 2−(∂ 2 h) 2)+ ξ, where ξ denotes a space-time white noise and λ> 0 …
Stationary stochastic Navier–Stokes on the plane at and above criticality
G Cannizzaro, J Kiedrowski - Stochastics and Partial Differential Equations …, 2024 - Springer
In the present paper, we study the fractional incompressible Stochastic Navier–Stokes
equation on R 2, formally defined as 0.1∂ tv=-1 2 (-Δ) θ v-λ v·∇ v+∇ p+∇⊥(-Δ) θ-1 2 ξ,∇ …
equation on R 2, formally defined as 0.1∂ tv=-1 2 (-Δ) θ v-λ v·∇ v+∇ p+∇⊥(-Δ) θ-1 2 ξ,∇ …
Stochastic homogenization with space-time ergodic divergence-free drift
B Fehrman - The Annals of Probability, 2024 - projecteuclid.org
We prove that diffusion equations with a space-time stationary and ergodic, divergence-free
drift homogenize in law to a deterministic stochastic partial differential equation with …
drift homogenize in law to a deterministic stochastic partial differential equation with …