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    "title": "Press and Schechter: estimate a hierarchy of gravitating condensations",
    "summary": "Press and Schechter develop a statistical model connecting small gravitating seeds to a growing condensation mass spectrum, with a Gaussian-tail construction, a surviving maximum-variance self-similar branch and limited N-body tests.\n\nInstead of assuming that all galaxies start as large, smooth disturbances, Press and Schechter ask whether smaller gravitating lumps can build larger structures. They estimate how fluctuations in a volume lead to bound condensations in an expanding universe and obtain a mass distribution with a power-law small-mass part and an exponential cutoff. For their randomly positioned, maximum-variance case, the characteristic condensed mass grows with the square of the expansion factor. The argument uses a spherical accretion estimate to account for initially underdense material and assumes that overlap errors are only of order unity. It is a useful statistical model, not an exact count of real galaxies. Two1000-particle experiments provide tentative numerical support and suggest nonlinear growth effects. A note added in proof accepts Peebles’s correction: the more ordered initial-distribution branch has an invalid energy argument and its stated scaling formulas must not be retained. Later excursion-set theory offers a distinct first-crossing justification under specified filters; that later work remains separately credited.",
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      "statement": "# Press and Schechter: estimate a hierarchy of gravitating condensations\n\nPress and Schechter develop a statistical model connecting small gravitating seeds to a growing condensation mass spectrum, with a Gaussian-tail construction, a surviving maximum-variance self-similar branch and limited N-body tests.\n\nInstead of assuming that all galaxies start as large, smooth disturbances, Press and Schechter ask whether smaller gravitating lumps can build larger structures. They estimate how fluctuations in a volume lead to bound condensations in an expanding universe and obtain a mass distribution with a power-law small-mass part and an exponential cutoff. For their randomly positioned, maximum-variance case, the characteristic condensed mass grows with the square of the expansion factor. The argument uses a spherical accretion estimate to account for initially underdense material and assumes that overlap errors are only of order unity. It is a useful statistical model, not an exact count of real galaxies. Two1000-particle experiments provide tentative numerical support and suggest nonlinear growth effects. A note added in proof accepts Peebles’s correction: the more ordered initial-distribution branch has an invalid energy argument and its stated scaling formulas must not be retained. Later excursion-set theory offers a distinct first-crossing justification under specified filters; that later work remains separately credited.\n\n## Scientific scope\n\nThe mass-distribution model uses specified Gaussian initial fluctuations, collapse thresholds and approximations. Its counting/normalization and scale-to-mass mapping are model assumptions, not an exact physical collapse proof. Nonlinear dynamics, mergers and finite simulations need further evidence. The later excursion-set first-crossing derivation is separately credited.\n\n## People and systems\n\nWilliam H. Press; Paul Schechter\n\n\n\n## Original sources\n\n- [William H. Press/Paul Schechter1974original425-438includingnoteaddedproof](https://adsabs.harvard.edu/pdf/1974ApJ...187..425P)\n- [Bond/Cole/Efstathiou/Kaiser1991: distinctexcursion-set first-crossing approach](https://articles.adsabs.harvard.edu/pdf/1991ApJ...379..440B)\n",
      "summary": "Press and Schechter develop a statistical model connecting small gravitating seeds to a growing condensation mass spectrum, with a Gaussian-tail construction, a surviving maximum-variance self-similar branch and limited N-body tests.\n\nInstead of assuming that all galaxies start as large, smooth disturbances, Press and Schechter ask whether smaller gravitating lumps can build larger structures. They estimate how fluctuations in a volume lead to bound condensations in an expanding universe and obtain a mass distribution with a power-law small-mass part and an exponential cutoff. For their randomly positioned, maximum-variance case, the characteristic condensed mass grows with the square of the expansion factor. The argument uses a spherical accretion estimate to account for initially underdense material and assumes that overlap errors are only of order unity. It is a useful statistical model, not an exact count of real galaxies. Two1000-particle experiments provide tentative numerical support and suggest nonlinear growth effects. A note added in proof accepts Peebles’s correction: the more ordered initial-distribution branch has an invalid energy argument and its stated scaling formulas must not be retained. Later excursion-set theory offers a distinct first-crossing justification under specified filters; that later work remains separately credited.",
      "title": "Press and Schechter: estimate a hierarchy of gravitating condensations"
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