6 papers
One-Dimensional Divergence-Type Jacobi Operators Driven by The Doubling Map
Long Li, Wei Wang, Shiwen Zhang
We study one-dimensional Jacobi operators of divergence-gradient type on , with coefficients generated by the doubling map, $a_n(x)=a(2^n x \mathrm{mod…
Edge localization and Lifshitz tails for graphs with Ahlfors regular volume growth
Laura Shou, Wei Wang, Shiwen Zhang
In this work, we study the Anderson model on graphs with Ahlfors -regular volume growth. We show that, under mild regularity assumptions of the random distribution, Lifshitz-tai…
Upper and Lower Bounds for The Quantum Dynamics of One-Dimensional Divergence-Type Random Jacobi Operators
Long Li, Wei Wang, Shiwen Zhang
We study quantum transport for the discrete one-dimensional random Jacobi operator of divergence-gradient type. For strictly positive and bounded random variables, we analyze the q…
Spectrum and Lifshitz tails for the Anderson model on the Sierpinski gasket graph
Laura Shou, Wei Wang, Shiwen Zhang
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…
Landscape estimates of the integrated density of states for Jacobi operators on graphs
Laura Shou, Wei Wang, Shiwen Zhang
We show the integrated density of states for a variety of Jacobi operators on graphs, such as the Anderson model and random hopping models on graphs with Gaussian heat kernel bound…
Landscape approximation of the ground state eigenvalue for graphs and random hopping models
Laura Shou, Wei Wang, Shiwen Zhang
We consider the localization landscape function and ground state eigenvalue for operators on graphs. We first show that the maximum of the landscape function is comparable…