  We use numerical simulations to predict the soft X-ray ([0.4-0.6] keV) and
Sunyaev-Zeldovich signal (at 150 GHz) from the large scale structure in the
Universe and then compute 2-point statistics to study the spatial distribution
and time evolution of the signals. The average X-ray signal predicted for the
WHIM is in good agreement with observational constraints that set it at about
10% of the total Diffuse X-ray Background. The characteristic angle computed
with the Autocorrelation Function is of the order of some arcminutes and
becomes smaller at higher redshift. The power spectrum peak of the SZ due to
the WHIM is at l~10000 and has amplitude of ~0.2 muK^2, about one order of
magnitude below the signal measured with telescopes like Planck, ACT, and SPT.
Even if the high-redshift WHIM signal is too weak to be detected using X-rays
only, the small-scale correlation between X-ray and SZ maps is dominated by the
high-redshift WHIM. This makes the analysis of the SZ signal in support of
X-rays a promising tool to study the early time WHIM.
