Author

P. Lamarre

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Preprint Aug 2026

The Parabolic Anderson Model's Total Mass at Small Times: Geometry, Fluctuations, and Renormalization

Let $D\subset\mathbb R^d$ be a bounded domain, let $\kappa>0$ be fixed, and let $W$ be a fractional Brownian sheet on $\mathbb R\times\mathbb R^d$. Consider the Stratonovich parabolic Anderson model (PAM) $\partial_tu_\kappa=(\frac12\Delta+\kappa W')u_\kappa$ with Dirichlet boundary condition on $D$ and the flat initia...

P. Lamarre, Yuanyuan Pan · 0 citations

Preprint Jul 2026

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...

Youssef Djellouli, P. Lamarre · 0 citations