Spectrum and Lifshitz Tails for the Anderson Model on the Sierpinski Gasket Graph
发布时间：2024年12月20日
浏览次数：76
发布者: Wenqiong Li
主讲人： 张世文（马萨诸塞大学洛厄尔分校）
活动时间： 从 2024-12-23 15:00 到 16:00
场地： 北京国际数学研究中心，镜春园78号院（怀新园）78201室
There are many works in physics literature about the Anderson model and other random Hamiltonians on fractals, but limited work has been done in math literature. In this talk, we consider the Anderson model on the Sierpinski gasket graph, a notable example of fractals. We first identify the almost sure spectrum of the Anderson model when the support of the random potential has no gaps. We then prove the existence of the integrated density states of the Anderson model and show that it has Lifshitz tails with Lifshitz exponent determined by the ratio of the volume growth rate and the random walk dimension of the Sierpinski gasket graph. The talk is based on a recent joint work with Laura Shou (UMD) and Wei Wang (ICMSEC).
