Abstract:
The surprising connection between a one-dimensional gravitationally interacting gas of sticky
particles and the convex minorant process generated by Brownian motion on $[0,1]$ is studied. A study is made of the dynamics of this 1-D gas system by identifying three distinct clustering regimes and the time scales at which they occur. At the critical moment of time the mass distribution of the gas can be computed in terms of functionals of the convex minorant process.
Citation:
T. M. Suidan, “A one-dimensional gravitationally interacting gas and the convex minorant of Brownian motion”, Russian Math. Surveys, 56:4 (2001), 687–708
\Bibitem{Sui01}
\by T.~M.~Suidan
\paper A~one-dimensional gravitationally interacting gas and the convex minorant of Brownian motion
\jour Russian Math. Surveys
\yr 2001
\vol 56
\issue 4
\pages 687--708
\mathnet{http://mi.mathnet.ru/eng/rm416}
\crossref{https://doi.org/10.1070/RM2001v056n04ABEH000416}
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Linking options:
https://www.mathnet.ru/eng/rm416
https://doi.org/10.1070/RM2001v056n04ABEH000416
https://www.mathnet.ru/eng/rm/v56/i4/p73
This publication is cited in the following 9 articles:
Pitman J., Bravo G.U., “The Convex Minorant of a Levy Process”, Ann. Probab., 40:4 (2012), 1636–1674
Majumdar S.N., Mallick K., Sabhapandit S., “Statistical properties of the final state in one-dimensional ballistic aggregation”, Phys. Rev. E (3), 79:2 (2009), 021109, 14 pp.
Vysotsky V.V., “Clustering in a stochastic model of one-dimensional gas”, Ann. Appl. Probab., 18:3 (2008), 1026–1058
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
Wolansky G., “Dynamics of a system of sticking particles of finite size on the line”, Nonlinearity, 20:9 (2007), 2175–2189
Isozaki Y., “On some laws of iterated logarithm for Burgers turbulence with Brownian initial data based on the concave majorant”, Osaka J. Math., 43:2 (2006), 239–261
V. V. Vysotsky, “Energy and number of clusters in stochastic systems of sticky gravitating particles”, Theory Probab. Appl., 50:2 (2006), 265–283
Lifshits M., Shi Zhan, “Aggregation rates in one-dimensional stochastic systems with adhesion and gravitation”, Ann. Probab., 33:1 (2005), 53–81
L. V. Kuoza, M. A. Lifshits, “Aggregation in one-dimensional gas model with stable initial data”, J. Math. Sci. (N. Y.), 133:3 (2006), 1298–1307
Citation in format AMSBIB
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