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Corrigendum to “Harmonic analysis on perturbed Cayley trees”. (English) Zbl 1307.47012
Summary: Due to the boundary effects, the standard definition of the integrated density of the states (i.d.s. for short) used in [the author, ibid. 261, No. 3, 604–634 (2011; Zbl 1229.47020)], does not work for nonamenable graphs like Cayley trees and density zero perturbations of those. On the other hand, Proposition 2.3 in the mentioned paper works under the right definition we are going to describe, and which is useful for all the applications. For the sake of completeness and the convenience of the reader, we also show that both the definitions coincide in the amenable case.

MSC:
47A55 Perturbation theory of linear operators
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
94C15 Applications of graph theory to circuits and networks
05C90 Applications of graph theory
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[1] Fidaleo, F., Harmonic analysis on perturbed Cayley trees, J. funct. anal., 261, 3, 604-634, (2011) · Zbl 1229.47020
[2] Fidaleo, F.; Guido, D.; Isola, T., Bose Einstein condensation on inhomogeneous amenable graphs, Infin. dimens. anal. quantum probab. relat. top., 14, 149-197, (2011) · Zbl 1223.82012
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