Cosmic Mass Functions from Gaussian Stochastic Diffusion Processes

Details Cosmic Mass Functions from Gaussian Stochastic Diffusion Processes Cosmic Mass Functions from Gaussian Stochastic Diffusion Processes

2001-02-26

arxiv.org/abs/astro-ph/0102439v1

Astronomy and Astrophysics

Astrophysics

17 pages, 8 figures, accepted for publication in Astronomy and Astrophysics, also available at http://www.xray.mpe.mpg.de/th

Scientific paper

10.1051/0004-6361:20010282

Gaussian stochastic diffusion processes are used to derive cosmic mass functions. To get analytic relations previous studies exploited the sharp $k$-space filter assumption yielding zero drift terms in the corresponding Fokker-Planck (Kolmogorov's forward) equation and thus simplifying analytic treatments significantly (excursion set formalism). In the present paper methods are described to derive for given diffusion processes and Gaussian random fields the corresponding mass and filter functions by solving the Kolmogorov's forward and backward equations including nonzero drift terms. This formalism can also be used in cases with non-sharp $k$-space filters and for diffusion processes exhibiting correlations between different mass scales.

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