Between 2008 and 2011, the IceCube Neutrino Observatory detected over $10^5$ neutrino events, for which the arrival directions, energies of secondary muons and angular positional errors have been determined. First, the IceCube Neutrino Observatory is briefly presented. The theory of the correlation analysis for spherical sky maps and the standard pseudo-$C_\ell$ power spectrum estimator are then presented. The data from the IceCube observatory are then correlated with it self and with other astrophysical maps of potential relevance. The astrophysical maps were chosen without theoretical prejudice. The auto and cross-correlations analyzed in this work do not show any evidence for a non-zero correlation.
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