We use mathematical methods based on generating functions to study the statistical properties of the black hole degeneracy spectrum in loop quantum gravity. In particular we will study the persistence of the observed effective quantization of the entropy as a function of the horizon area. We will show that this quantization disappears as the area increases despite the existence of black hole configurations with a large degeneracy. The methods that we describe here can be adapted to the study of the statistical properties of the black hole degeneracy spectrum for all the existing proposals to define black hole entropy in loop quantum gravity. © 2011 American Physical Society.

This work has been supported by the Spanish MICINN research Grant No. FIS2009- 11893 and the Consolider-Ingenio 2010 Program CPAN (CSD2007-00042).

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