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arXiv · 1106.5724

Uniform existence of the integrated density of states on metric Cayley graphs

Felix Pogorzelski·Fabian Schwarzenberger·Christian Seifert
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Abstract

Given a finitely generated amenable group we consider ergodic random Schrödinger operators on a Cayley graph with random potentials and random boundary conditions. We show that the normalised eigenvalue counting functions of finite volume parts converge uniformly. The integrated density of states as the limit can be expressed by a Pastur-Shubin formula. The spectrum supports the corresponding measure and discontinuities correspond to the existence of compactly supported eigenfunctions.

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Felix Pogorzelski, Fabian Schwarzenberger, Christian Seifert. 2014-02-17. Uniform existence of the integrated density of states on metric Cayley graphs. https://doi.org/10.1007/s11005-013-0626-5

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