  Non-Gaussian statistics of late-time cosmological fields contain information
beyond that captured in the power spectrum. Here we focus on one such example:
the one-point probability distribution function (PDF) of the thermal
Sunyaev-Zel'dovich (tSZ) signal in maps of the cosmic microwave background
(CMB). It has been argued that the one-point PDF is a near-optimal statistic
for cosmological constraints from the tSZ signal, as most of the constraining
power in tSZ $N$-point functions is contained in their amplitudes (rather than
their shapes), which probe differently-weighted integrals over the halo mass
function. In this paper, we develop a new analytic halo model for the tSZ PDF,
discarding simplifying assumptions made in earlier versions of this approach.
In particular, we account for effects due to overlaps of the tSZ profiles of
different halos, as well as effects due to the clustering of halos. We verify
the accuracy of our analytic model via comparison to numerical simulations. We
demonstrate that this more accurate model is necessary for the analysis of the
tSZ PDF in upcoming CMB experiments. The novel formalism developed here may be
useful in modeling the one-point PDF of other cosmological observables, such as
the weak lensing convergence field.
