  This work presents a scenario of ultra-high energy cosmic ray source
distribution where a nearby source is solely responsible for the anisotropies
in arrival directions of cosmic rays while the rest of the sources contribute
only isotropically. An analytical approach focused on large-scale anisotropies,
which are influenced by deflections in a Kolmogorov-type turbulent magnetic
field, is employed to provide more general results. When the recent Pierre
Auger Observatory angular power spectrum above 8 EeV is used the restricted
model gives, under the assumption of the small angle approximation, a solution
where the RMS deflection with respect to the line of sight is $\alpha_{\rm rms}
= \left(50^{+11}_{-10}\right)^\circ$, while the relative flux from the single
source $\eta=0.03\pm 0.01$. Furthermore, the solution can be translated into
constraints on the source distance, luminosity, and extra-galactic magnetic
field strength. For Centaurus A and the Virgo cluster the required relation
between the coherence length and the RMS magnetic field strength is obtained: a
coherence length of $~\sim 100\,\mathrm{kpc}$ would imply the RMS field
strength around $1\,\mathrm{nG}$ for iron dominated and above $10\,\mathrm{nG}$
for proton dominated composition. We also performed trajectory simulations with
our publicly available code CRPropa to show that our analytical model can serve
as a good approximation as long as the deflections in cosmic magnetic fields
can be described as a random walk. The simulations showed that generally
structured fields tend to suppress large-scale anisotropies, especially the
dipole, compared to anisotropies at smaller scales described by higher
multipoles.
