4 problems

Let $J$ be a kernel that decays sufficiently fast, and let $F_\varepsilon$ denote the equilibrium of the corresponding nonlocal Fokker–Planck equation. Poisson-like tail conjecture…

Let $M,N$ and $m,n$ be numbers satisfying the scaling in Theorem. Write $x=x_2-x_1$ for the separation parameter. Cubic upper-tail conjecture. As $x$ becomes large, the probability…

Fix $x\in\mathbb{R}^d$, $\omega\in\Omega$, and $n\geq 0$. Let $P_{y,\omega}$ denote the law of the diffusion started at $y$ in environment $\omega$, and let $X^*_{L_n^2}$ be its ma…

the exponential maximal-excursion tail control asserts