Yuanyuan Pan

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...