The critical 2d stochastic heat flow
We consider directed polymers in random environment in the critical dimension d= 2,
focusing on the intermediate disorder regime when the model undergoes a phase transition …
focusing on the intermediate disorder regime when the model undergoes a phase transition …
A class of supercritical/critical singular stochastic PDEs: existence, non-uniqueness, non-Gaussianity, non-unique ergodicity
We study the surface quasi-geostrophic equation with an irregular spatial perturbation∂ t θ+
u⋅∇ θ=− ν (− Δ) γ/2 θ+ ζ, u=∇⊥(− Δ)− 1 θ, on [0,∞)× T 2, with ν⩾ 0, γ∈[0, 3/2) and ζ∈ …
u⋅∇ θ=− ν (− Δ) γ/2 θ+ ζ, u=∇⊥(− Δ)− 1 θ, on [0,∞)× T 2, with ν⩾ 0, γ∈[0, 3/2) and ζ∈ …
Fluctuations for non-Hermitian dynamics
P Bourgade, G Cipolloni, J Huang - arXiv preprint arXiv:2409.02902, 2024 - arxiv.org
We prove that under the Brownian evolution on large non-Hermitian matrices the log-
determinant converges in distribution to a 2+ 1 dimensional Gaussian field in the Edwards …
determinant converges in distribution to a 2+ 1 dimensional Gaussian field in the Edwards …
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 …
Surface quasi-geostrophic equation perturbed by derivatives of space-time white noise
We consider a family of singular surface quasi-geostrophic equations∂ tθ+ u·∇ θ=− ν (−)
γ/2θ+(−) α/2ξ, u=∇⊥(−)− 1/2θ, on [0,∞)× T2, where ν⩾ 0, γ∈[0, 3/2), α∈[0, 1/4) and ξ is a …
γ/2θ+(−) α/2ξ, u=∇⊥(−)− 1/2θ, on [0,∞)× T2, where ν⩾ 0, γ∈[0, 3/2), α∈[0, 1/4) and ξ is a …
Stochastic heat flow by moments
LC Tsai - arXiv preprint arXiv:2410.14657, 2024 - arxiv.org
The critical two-dimensional Stochastic Heat Flow (SHF) is the scaling limit of the directed
polymers in random environments and the noise-mollified Stochastic Heat Equation (SHE) …
polymers in random environments and the noise-mollified Stochastic Heat Equation (SHE) …
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 …
A forward-backward SDE from the 2D nonlinear stochastic heat equation
We consider a nonlinear stochastic heat equation in spatial dimension d= 2, forced by a
white-in-time multiplicative Gaussian noise with spatial correlation length ε> 0 but divided by …
white-in-time multiplicative Gaussian noise with spatial correlation length ε> 0 but divided by …
The stationary AKPZ equation: logarithmic superdiffusivity
G Cannizzaro, D Erhard… - Communications on Pure …, 2023 - Wiley Online Library
We study the two‐dimensional Anisotropic KPZ equation (AKPZ) formally given by∂ t H= 1 2
Δ H+ λ ((∂ 1 H) 2−(∂ 2 H) 2)+ ξ,* 3.4 pc ∂ _t H= 1 2 Δ H+ λ ((∂ _1 H)^ 2-(∂ _2 H)^ 2)+ ξ …
Δ H+ λ ((∂ 1 H) 2−(∂ 2 H) 2)+ ξ,* 3.4 pc ∂ _t H= 1 2 Δ H+ λ ((∂ _1 H)^ 2-(∂ _2 H)^ 2)+ ξ …
Multiplicative SHE limit of random walks in space–time random environments
S Das, H Drillick, S Parekh - Probability Theory and Related Fields, 2024 - Springer
We show that under a certain moderate deviation scaling, the multiplicative-noise stochastic
heat equation (SHE) arises as the fluctuations of the quenched density of a 1D random walk …
heat equation (SHE) arises as the fluctuations of the quenched density of a 1D random walk …