  The ISM is governed by supersonic turbulence on a range of scales. We use
this to develop a rigorous excursion-set model for the formation and time
evolution of dense gas structures (GMCs, massive clumps, and cores). Supersonic
turbulence drives the density distribution to a lognormal with dispersion
increasing with Mach number; we generalize this to include scales >h (the disk
scale height), and use it to construct the statistical properties of the
density field smoothed on a scale R. We then compare conditions for
self-gravitating collapse including thermal, turbulent, and rotational support.
We show this becomes a well-defined barrier crossing problem. As such, an exact
'bound object mass function' can be derived, from scales of the sonic length to
above the disk Jeans mass. This agrees remarkably well with observed GMC mass
functions in the MW and other galaxies; the only inputs are the mass and size
of the galaxies (to normalize the model). This explains the mass function
cutoff and its power-law slope (close to, but shallower than, -2). The model
also predicts the linewidth-size and size-mass relations of clouds and the
dependence of their residuals on surface density/pressure. We use this to
predict the spatial correlation function/clustering of clouds and star
clusters; these also agree well with observations. We predict the size/mass
function of ISM 'bubbles' or 'holes', and show this can account for observed HI
hole distributions without any local feedback. We generalize the model to
construct time-dependent 'merger/fragmentation trees' which can be used to
follow cloud evolution and construct semi-analytic models for the ISM. We
provide explicit recipes to construct the trees. We use a simple example to
show that, if clouds are not destroyed in ~1-5 crossing times, then all ISM
mass would be trapped in collapsing objects even if the large-scale turbulence
were maintained.
