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

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

Bibliographic databases:

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
\Bibitem{Vys05} \by V.~V.~Vysotsky \paper Energy and number of clusters in stochastic systems of sticky gravitating particles \jour Teor. Veroyatnost. i Primenen. \yr 2005 \vol 50 \issue 2 \pages 241--265 \mathnet{http://mi.mathnet.ru/tvp106} \crossref{https://doi.org/10.4213/tvp106} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2221711} \zmath{https://zbmath.org/?q=an:1100.82018} \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} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000238760000007} 

• http://mi.mathnet.ru/eng/tvp106
• https://doi.org/10.4213/tvp106
• http://mi.mathnet.ru/eng/tvp/v50/i2/p241

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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
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
3. Vysotsky V.V., “Clustering in a stochastic model of one–dimensional gas”, Annals of Applied Probability, 18:3 (2008), 1026–1058
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
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