4 problems

Diffusive-limit conjecture. As $\eta$ goes to zero, the processes $({\mathbf{X}}^\eta_t({\mathbf{x}}))_{t\ge 0}$ converge in law to the $2$-dimensional process…

Let $d\in\{2,3\}$. Let $u\in C^0([0,1];C^\alpha(\mathbb T^d))\cap C^\alpha([0,1];C^0(\mathbb T^d))$ be a weak solution of the incompressible Euler equations, for some Hölder expone…

Let $(W_n,G_n)$ be the barycentric excluded-volume random walk described in the paper, with $W_n\in\mathbb R^2$ its position, and let $\|\cdot\|$ denote Euclidean norm. Let…

Let $\gamma\in(\frac12,1)$, let $v:X\to\mathbb{R}^d$ and $h:X\to G$ be the observable and cocycle from the system, and let $\operatorname{Fix} h(0)=\{w\in\mathbb{R}^d:h(0)w=w\}$. W…