  We used magneto-hydrodynamical cosmological simulations to investigate the
cross-correlation between different observables (i.e. X-ray emission,
Sunyaev-Zeldovich signal at 21 cm, HI temperature decrement, diffuse
synchrotron emission and Faraday Rotation) as a probe of the diffuse matter
distribution in the cosmic web. We adopt an uniform and simplistic approach to
produce synthetic observations at various wavelengths, and we compare the
detection chances of different combinations of observables correlated with each
other and with the underlying galaxy distribution in the volume. With presently
available surveys of galaxies and existing instruments, the best chances to
detect the diffuse gas in the cosmic web outside of halos is by
cross-correlating the distribution of galaxies with Sunyaev-Zeldovich
observations. We also find that the cross-correlation between the galaxy
network and the radio emission or the Faraday Rotation can already be used to
limit the amplitude of extragalactic magnetic fields, well outside of the
cluster volume usually explored by existing radio observations, and to probe
the origin of cosmic magnetism with the future generation of radio surveys.
