Spectrum and Lifshitz Tails for the Anderson Model on the Sierpinski Gasket Graph
Abstract
Abstract. 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 a Lifshitz exponent determined by the ratio of the volume growth rate and the random walk dimension of the Sierpinski gasket graph.
Fields of Study & Subjects
Quantum chaos and dynamical systems
Algebraic structures and combinatorial models
Graph theory and applications
Publication details
- Journal / source
- SIAM Journal on Mathematical Analysis
- Volume
- 58
- Issue
- 3
- Pages
- 3082–3112
- Publication date
- 19 June 2026
- Language
- EN