4 problems

Fix $u,v\in\R$. Let $h_0,\tilde h_0\in\operatorname{C}([0,1])$ be arbitrary random functions on the same probability space, and let $\xi$ be white noise on $\mathbb{R}\times[0,1]$.…

For any $\delta>0$, let $\mathcal{C}_{\mathfrak{s};\mathrm{loc}}^{-\delta}(\mathbf{R}_{>0}\times\mathbf{T}^{2})$ and $\mathcal{C}^{-\delta}(\mathbf{T}^{2})$ denote the correspondin…

Let $u$, $\lambda$, and $D$ satisfy the effective-coupling condition from the paper, and let $(h^\varepsilon)_{\varepsilon>0}$ denote the rescaled KPZ fields, with…

Let $g$ be the function used to define $Q_{t,\beta}(\sigma)$, let $\mathfrak{L}_i$ denote the corresponding coefficients, and let $\mathbf{n}=(n_1,\ldots,n_{r+2-2q})$. If the disti…