An Invitation to Trees of Finite Cone Type: Random and Deterministic Operators

M. Keller, D. Lenz, S. Warzel

2015, v.21, №3, 557-574

ABSTRACT

Trees of finite cone type have appeared in various contexts. In
particular, they come up as simplified models of regular
tessellations of the hyperbolic plane. The spectral theory of the
associated Laplacians can thus be seen as induced by geometry. Here
we give an introduction focusing on background and then turn to
recent results for (random) perturbations of trees of finite cone
type and their spectral theory.

Keywords: trees, Laplacian, spectrum, random operator

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