We prove the existence and establish the Lifschitz singularity of the integrated density of states for certain random Hamiltonians \(H^\omega =H_0+V^\omega \) on fractal spaces of infinite diameter. The kinetic term \(H_0\) is given by \(\phi (-{\mathcal {L}}),\) where \({\mathcal {L}}\) is the Laplacian on the fractal and \(\phi \) is a completely monotone function satisfying some mild regularity conditions. The random potential \(V^\omega \) is of alloy-type.

中文翻译：

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嵌套分形的安德森模型的状态密度

我们证明了无限直径分形空间上某些随机哈密顿量\(H^\omega =H_0+V^\omega \)的存在性并建立了积分状态密度的 Lifschitz 奇点。动力学项\(H_0\)由\(\phi (-{\mathcal {L}}),\)给出，其中\({\mathcal {L}}\)是分形上的拉普拉斯算子，而\(\ phi \)是一个完全单调的函数，满足一些温和的规律性条件。随机势\(V^\omega \)是合金型的。