We have determined the currently allowed regions of the parameter spaces of two representative models of diffuse neutrino flux from active galactic nuclei ( AGN ) : one by Koers & Tinyakov ( KT ) and another by Becker & Biermann ( BB ) .
Our observable has been the number of upgoing muon-neutrinos expected in the 86-string IceCube detector , after 5 years of exposure , in the range 10 ^ { 5 } \leq E _ { \nu } / \text { GeV } \leq 10 ^ { 8 } .
We have used the latest estimated discovery potential of the IceCube-86 array at the 5 \sigma level to determine the lower boundary of the regions , while for the upper boundary we have used either the AMANDA upper bound on the neutrino flux or the more recent preliminary upper bound given by the half-completed IceCube-40 array ( IC40 ) .
We have varied the spectral index of the proposed power-law fluxes , \alpha , and two parameters of the BB model : the ratio between the boost factors of neutrinos and cosmic rays , \Gamma _ { \nu } / \Gamma _ { \text { CR } } , and the maximum redshift of the sources that contribute to the cosmic-ray flux , z _ { \text { CR } } ^ { \max } .
For the KT model , we have considered two scenarios : one in which the number density of AGN does not evolve with redshift and another in which it evolves strongly , following the star formation rate .
Using the IC40 upper bound , we have found that the models are visible in IceCube-86 only inside very thin strips of parameter space and that both of them are discarded at the preferred value of \alpha = 2.7 obtained from fits to cosmic-ray data .
Lower values of \alpha , notably the values 2.0 and 2.3 proposed in the literature , fare better .
In addition , we have analysed the capacity of IceCube-86 to discriminate between the models within the small regions of parameter space where both of them give testable predictions .
Within these regions , discrimination at the 5 \sigma level or more is guaranteed .