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January 2005 Aggregation rates in one-dimensional stochastic systems with adhesion and gravitation
Mikhail Lifshits, Zhan Shi
Ann. Probab. 33(1): 53-81 (January 2005). DOI: 10.1214/009117904000000900

Abstract

We consider one-dimensional systems of self-gravitating sticky particles with random initial data and describe the process of aggregation in terms of the largest cluster size Ln at any fixed time prior to the critical time. The asymptotic behavior of Ln is also analyzed for sequences of times tending to the critical time. A phenomenon of phase transition shows up, namely, for small initial particle speeds (“cold” gas) Ln has logarithmic order of growth while higher speeds (“warm” gas) yield polynomial rates for Ln.

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Mikhail Lifshits. Zhan Shi. "Aggregation rates in one-dimensional stochastic systems with adhesion and gravitation." Ann. Probab. 33 (1) 53 - 81, January 2005. https://doi.org/10.1214/009117904000000900

Information

Published: January 2005
First available in Project Euclid: 11 February 2005

zbMATH: 1096.60041
MathSciNet: MR2118859
Digital Object Identifier: 10.1214/009117904000000900

Subjects:
Primary: 60F10 , 60K35 , 70F10

Keywords: adhesion , Aggregation , Gravitation , large deviation , Particle system , self-gravitating gas , Sticky particles

Rights: Copyright © 2005 Institute of Mathematical Statistics

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Vol.33 • No. 1 • January 2005
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