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We study the one-point probability distribution function (PDF) for matterdensity averaged over spherical cells. The leading part to the PDF is definedby spherical collapse dynamics, whereas the next-to-leading part comes from theintegration over fluctuations around the saddle-point solution. The lattercalculation receives sizable contributions from short modes and must berenormalized. We propose a new approach to renormalization by modeling theeffective stress-energy tensor for short perturbations. The model containsthree free parameters. Two of them are related to the counterterms in theone-loop matter power spectrum and bispectrum, one more parameterizes theirredshift dependence. This relation can be used to impose priors in fitting themodel to the PDF data. We confront the model with the results ofhigh-resolution N-body simulations and find excellent agreement for cell radii$r_*\geq 10\,{\rm Mpc}/h$ at all redshifts down to $z=0$. Discrepancies at afew per cent level are detected at low redshifts for $r_*\leq 10\,{\rm Mpc}/h$and are associated with two-loop corrections to the model.

Renormalizing one-point probability distribution function for cosmological counts in cells