  The Sunyaev-Zel'dovich (SZ) effect associated with pressure fluctuations of
the large scale structure gas distribution will be probed with current and
upcoming wide-field small angular scale cosmic microwave background
experiments. We study the generation of pressure fluctuations by baryons which
are present in virialized dark matter halos and by baryons present in small
overdensities. For collapsed halos, assuming the gas distribution is in
hydrostatic equilibrium with matter density distribution, we predict the
pressure power spectrum and bispectrum associated with the large scale
structure gas distribution by extending the dark matter halo approach which
describes the density field in terms of correlations between and within halos.
The projected pressure power spectrum allows a determination of the resulting
SZ power spectrum due to virialized structures. The unshocked photoionized
baryons present in smaller overdensities trace the Jeans-scale smoothed dark
matter distribution. They provide a lower limit to the SZ effect due to large
scale structure in the absence of massive collapsed halos. We extend our
calculations to discuss higher order statistics, such as bispectrum and
skewness in SZ data. The SZ-weak lensing cross-correlation is suggested as a
probe of correlations between dark matter and baryon density fields, while the
probability distribution functions of peak statistics of SZ halos in wide field
CMB data can be used as a probe of cosmology and non-Gaussian evolution of
large scale structure pressure fluctuations.
