Spectrum and Lifshitz Tails for the Anderson Model on the Sierpinski Gasket Graph
In this work, we study the Anderson model on the Sierpinski gasket graph. 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.
Authors
- Laura Shou (ORCID: https://orcid.org/0000-0001-8624-8063)
- Shiwen Zhang (ORCID: https://orcid.org/0000-0002-0117-4585)
- Wei Wang (ORCID: https://orcid.org/0000-0002-9532-6286)
Institutions
- University of Massachusetts Lowell (US)
- Academy of Mathematics and Systems Science (CN)
- University of Maryland, College Park (US)
Publication Details
- Journal
- SIAM Journal on Mathematical Analysis
- Published
- 2026-06-19
- DOI
- https://doi.org/10.1137/25m1769545
- Primary Topic
- Quantum chaos and dynamical systems
- Type
- preprint
- Field-Weighted Citation Impact
- 0.00
Funders
- National Science Foundation
- National Key Research and Development Program of China