Corrigendum to “Harmonic analysis on perturbed Cayley Trees” [J. Funct. Anal. 261 (3) (2011) 604–634]

Due to the boundary effects, the standard definition of the integrated density of the states (i.d.s. for short) used in F. Fidaleo, Harmonic analysis on perturbed Cayley Trees, J. Funct. Anal. 261 (3) (2011) 604–634], does not work for nonamenable graphs like Cayley Trees and density zero perturbations of those. On the other hand, Proposition 2.3 in the previous 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.