标题： 图上的雅可比算子的积分态密度的景观估计 显示英文标题

标题： Landscape estimates of the integrated density of states for Jacobi operators on graphs

摘要： 我们展示了在图上各种雅可比算子的积分态密度，例如在具有高斯热核界限的图上的安德森模型和随机跳跃模型，可以利用定位景观计数函数从上方和下方进行估计。这些图的具体例子包括堆叠和装饰晶格、对应于带状矩阵的图以及非周期性铺砌图。景观定律的上界部分也适用于分形谢尔宾斯基垫脚石图。作为景观定律的结果，我们获得了基于景观的证明，包括随机带状矩阵模型、某些在$\mathbb{Z}^d$上的键渗透哈密顿量以及某些图堆叠上的雅可比算子的利夫希茨尾部。我们还展示了引人入胜的数值模拟，探索了景观计数函数在各种模型中的行为。 显示英文摘要

摘要： 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 bounds, can be estimated from above and below in terms of the localization landscape counting function. Specific examples of these graphs include stacked and decorated lattices, graphs corresponding to band matrices, and aperiodic tiling graphs. The upper bound part of the landscape law also applies to the fractal Sierpinski gasket graph. As a consequence of the landscape law, we obtain landscape-based proofs of the Lifshitz tails in several models including random band matrix models, certain bond percolation Hamiltonians on $\mathbb{Z}^d$, and Jacobi operators on certain stacks of graphs. We also present intriguing numerical simulations exploring the behavior of the landscape counting function across various models.