| Speaker: | 杨寰宇 博士, 重庆大学 | | Inviter: | | | Title: | Geometric intermittency of continuum parabolic Anderson model with smooth Gaussion potential | | Time & Venue: | 2023.10.27 11:00 N613 | | Abstract: | We consider the parabolic Anderson model $\partial_tu=\Delta u+\xi u$ on $\mathbb{R}^d$ with smooth time-homogeneous Gaussian potential $\xi$ and initial value $u(0)=\delta_0$. Combining with the strategy of discrete parabolic Anderson model and the random polymer measure, we prove the geometric intermittency: with probability one, as $t\to\infty$, the total mass $\int_{\mathbb{R}^d} u(t,x)dx$ comes from some slow increasing, small and remote islands where the local principal eigenvalues of (Dirichlet) Anderson Hamiltonian $\Delta+\xi$ are closed to the principal eigenvalue of Anderson Hamiltonian on the box $(-t\log t, t\log t)^d$. This is a joint work with Nicolas Perkowski. | | | Affiliation: | | |
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