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Description
We study one-point probability distribution function (PDF) for averaged matter densities over spherical cells as a non-perturbative probe of the large-scale structure. The PDF is analytically modelled using a path integral framework. It contains a leading order contribution controlled by the spherically symmetric gravitational collapse dynamics, as well as higher order contributions coming from aspherical fluctuations. We investigate the sensitivity of the PDF to the shape of the window function by considering a family of radial window functions interpolating between the top-hat and Gaussian filters in coordinate space. We find that the sensitivity is rather mild suggesting that the PDF is robust against the precise choice of the filter. The results are compared to N-body simulations.