  The sources of ultra-high energy cosmic rays (UHECRs) are still one of the
main open questions in high-energy astrophysics. If UHECRs are accelerated in
astrophysical sources, they are expected to produce high-energy photons and
neutrinos due to the interaction with the surrounding astrophysical medium or
ambient radiation. In particular, neutrinos are powerful probes for the
investigation of the region of production and acceleration of UHECRs since they
are not sensitive to magnetic deflections nor to interactions with the
interstellar medium. The results of three different analyses that correlate the
very high-energy neutrino candidates detected by IceCube and ANTARES and the
highest-energy cosmic rays measured by the Pierre Auger Observatory and the
Telescope Array will be discussed. The first two analyses use a sample of
high-energy neutrinos from IceCube and ANTARES selected to have a significant
probability to be of astrophysical origin. The first analysis cross-correlates
the arrival directions of these selected neutrino events and UHECRs. The second
one is a stacked likelihood analysis assuming as stacked sources the
high-energy neutrino directions and looking for excesses in the UHECR data set
around the directions of the neutrino candidates. The third analysis instead
uses a larger sample of neutrinos selected to look for neutrino point-like
sources. It consists of a likelihood method that looks for excesses in the
neutrino point-source data set around the directions of the highest-energy
UHECRs.
