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Teor. Veroyatnost. i Primenen., 2005, Volume 50, Issue 2, Pages 241–265 (Mi tvp106)  

This article is cited in 4 scientific papers (total in 4 papers)

Energy and number of clusters in stochastic systems of sticky gravitating particles

V. V. Vysotsky

Saint-Petersburg State University

Abstract: We consider a one-dimensional model of a gravitational gas. The gas consists of $n$ particles whose initial positions and speeds are random. At collisions particles stick together, forming “clusters.” Our main goal is to study the properties of the gas as $n\to\infty$. We separately consider “cold gas” (each particle has zero initial speed) and “warm gas” (each particle has nonzero initial speed). For the cold gas, the asymptotics of the number of clusters $K_n(t)$ is studied. We also explore the kinetic energy $E_n(t)$. It is proved that the warm gas instantly “cools,” i.e., $E_n(+0)\to 0$ as $n\to\infty$.

Keywords: gravitational gas, sticky particles, nonelastic collisions, system of particles, number of clusters, energy.

DOI: https://doi.org/10.4213/tvp106

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English version:
Theory of Probability and its Applications, 2006, 50:2, 265–283

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Received: 11.08.2003

Citation: V. V. Vysotsky, “Energy and number of clusters in stochastic systems of sticky gravitating particles”, Teor. Veroyatnost. i Primenen., 50:2 (2005), 241–265; Theory Probab. Appl., 50:2 (2006), 265–283

Citation in format AMSBIB
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\by V.~V.~Vysotsky
\paper Energy and number of clusters in stochastic systems of sticky gravitating particles
\jour Teor. Veroyatnost. i Primenen.
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\vol 50
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\pages 241--265
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\elib{http://elibrary.ru/item.asp?id=9153121}
\transl
\jour Theory Probab. Appl.
\yr 2006
\vol 50
\issue 2
\pages 265--283
\crossref{https://doi.org/10.1137/S0040585X97981639}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. F. Zakharova, “Aggregation rates in one-dimensional stochastic gas model with finite polynomial moments of particle speeds”, J. Math. Sci. (N. Y.), 152:6 (2008), 885–896  mathnet  crossref  elib
    2. V. V. Vysotsky, “The area of exponential random walk and partial sums of uniform order statistics”, J. Math. Sci. (N. Y.), 147:4 (2007), 6873–6883  mathnet  crossref  mathscinet  zmath
    3. Vysotsky V.V., “Clustering in a stochastic model of one–dimensional gas”, Annals of Applied Probability, 18:3 (2008), 1026–1058  crossref  mathscinet  zmath  isi  scopus
    4. Ibragimov I.A. Lifshits M.A. Nazarov A.I. Zaporozhets D.N., “On the History of St. Petersburg School of Probability and Mathematical Statistics: II. Random Processes and Dependent Variables”, Vestn. St Petersb. Univ.-Math., 51:3 (2018), 213–236  crossref  isi  scopus
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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