Youssef Djellouli

Optimal Covariance Estimates for Schr\"odinger Semigroups with White Noise in $d=1,2$

For $d\in\{1,2\}$, let $H=-\frac{1}{2}\Delta + V +\xi$ be the random Schr\"odinger operator on $L^2(\mathbb{R}^d)$ where $\xi$ is a standard Gaussian white noise and $V$ is a deterministic potential with power-law growth at infinity. Using a Feynman-Kac formula for the trace of the Schr\"odinger semigroup, we give opti...