Recently, IceCube found evidence for a diffuse signal of astrophysical neutrinos in an energy range of $60\,\mathrm{TeV}$ to the $\mathrm{PeV}$-scale. The origin of those events, being a key to understanding the origin of cosmic rays, is still an unsolved question. So far, analyses have not succeeded to resolve the diffuse signal into point-like sources. Searches including a maximum-likelihood-ratio test, based on the reconstructed directions and energies of the detected down- and up-going neutrino candidates, were also performed on IceCube data leading to the exclusion of bright point sources. In this paper, we present two methods to search for faint neutrino point sources in three years of IceCube data, taken between 2008 and 2011. The first method is an autocorrelation test, applied separately to the northern and southern sky. The second method is a multipole analysis, which expands the measured data in the northern hemisphere into spherical harmonics and uses the resulting expansion coefficients to separate signal from background. With both methods, the results are consistent with the background expectation with a slightly more sparse spatial distribution, corresponding to an underfluctuation. Depending on the assumed number of sources, the resulting upper limit on the flux per source in the northern hemisphere for an $E^{-2}$ energy spectrum ranges from $1.5 ⋅ 10^{-8}\,\mathrm{GeV}/(\mathrm{cm}^2 \mathrm{s})$, in the case of one assumed source, to $4 ⋅ 10^{-10} \,\mathrm{GeV}/(\mathrm{cm}^2 \mathrm{s})$, in the case of $3500$ assumed sources. ; Comment: 35 pages, 16 figures, 1 table