1994/11/01 by A. Cavaliere, N. Menci · 1 citation
Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #astro-ph
paper · pdf · doi:10.1086/174833
Plain TEX, compressed and uuencoded, 30 pages, 4 figs upon request from [email protected]
openalex publication_date 1994/11/01 · arxiv created 1994/11/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a new approach to the statistics of the cosmic density field and to the mass distribution of bound structures, based on the formalism of Cayley trees. Our approach includes in one random process both fluctuations and interactions of the density perturbations. We connect tree-related quantities, like the partition function or its generating function, to the mass distribution. The Press & Schechter mass function and the Smoluchowski kinetic equation are naturally recovered as two limiting cases, corresponding to independent Gaussian fluctuations and to aggregation of high-contrast condensations, respectively. Numerical realizations of the complete random process on the tree yield an excess of large-mass objects relative to the Press & Schechter function. When interactions are fully effective, a power-law distribution with logarithmic slope - 2 is generated.