Yuanyuan Pan

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20232026

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math.PR2026

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

Pierre Yves Gaudreau Lamarre, Yuanyuan Pan

Let $D \subset R^{d}$ be a bounded domain, let $κ > 0$ be fixed, and let $W$ be a fractional Brownian sheet on $R \times R^{d}$ . Consider the Stratonovich parabolic A…

math.PR2025

On the Spectral Geometry and Small Time Mass of Anderson Models on Planar Domains

Pierre Yves Gaudreau Lamarre, Yuanyuan Pan

We consider the Anderson Hamiltonian (AH) and the parabolic Anderson model (PAM) with white noise and Dirichlet boundary condition on a bounded planar domain $D \subset R^{2}$ .…

math.PR2023

The damped wave equation and associated polymer

Yuanyuan Pan

Considering the damped wave equation with a Gaussian noise $F$ where $F$ is white in time and has a covariance function depending on spatial variables, we will see that this equati…