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tokens: universes can measure very different power spectra of events, just because of cosmic variance. This effect dominates any dependence of predicted anisotropies on the class of EGMF models studied here, limiting the possibility of inferring the origin of EGMF based on the observed properties of UHECRs. It also stresses the importance of a realistic characterization of the local environment of the observer to interpret observations on Earth. This can be studied further making use of ‘Constrained Simulations’ of the local Universe (e.g. Jasche Wandelt 2013 ; Sorce et al. 2016 ). 3.3 Separation angle Abreu et al. ( 2010 ) investigated the anisotropy of the UHECR arrival signal by considering the angular distance of events from Cen A. Due to its similarity, all the graphics presented in this section, if not stated otherwise, are shown for observer ID61 whose closest source is at ∼4Mpc distance. The separation angle of pairs of events in Fig. 13 was computed via the scalar product of their arrival direction, i.e. the normalized negative momentum vector of the UHECRs at time of observation. The theoretical prediction for isotropy for the distribution of events over a sphere is given by the cumulative sine function and is in good agreement with the simulated isotropic cases. We can also predict the influence of the observer effect (cf. Section 2.3 ) for the signal of the closest source. To do so, we produced a test simulation without magnetic fields with a single source of UHECRs at a distance comparable to that of the closest source for observer ID61. The separation angle function of this test gives our prediction for the finite observer effect for pairs of events that both originated from the closest source. Figure 13. The fraction of pairs of observed events, E > 58, 100 EeV (left, right), separated by less than the given angle. The coloured lines indicate the magnetic field model, the error bars show the Poissonian noise. The thick black line shows the isotropic plus the geometric prediction. The left-hand panel of Fig. 13 can be compared with fig. 8 in Abreu et al. ( 2010 ). For events above E > 58 EeV there is no significant deviation from isotropy, but for E > 100 EeV there is a clear excess. This is expected because, due to lower average travel distances at higher energies, there is a higher number of events that originated from the closest source. The influence of the geometric effect changes the form of this plot by flattening the slope in the low separation part. We emphasize that this actually affects all events from close-by sources, while our geometric prediction only considers those from the closest source. None the less, there is a significant difference between the magnetic field models: the magnetic field free case ( b0 , black) and the simulation with the lowest magnetization ( agnl , purple, cf. Fig. 1 ) show the strongest deviation from isotropy. However, for other observers the case is different and the presence of nearby sources