Spectrum and Lifshitz Tails for the Anderson Model on the Sierpinski Gasket Graph
Time: 2024-12-20
Published By: Wenqiong Li
Speaker(s): Shiwen Zhang (University of Massachusetts Lowell)
Time: 15:00-16:00 December 23, 2024
Venue: Room 78201, Jingchunyuan 78, BICMR
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).
