Clustering in a stochastic model of one-dimensional gas
Vladislav V. Vysotsky
Source: Ann. Appl. Probab. Volume 18, Number 3
(2008), 1026-1058.
Abstract
We give a quantitative analysis of clustering in a stochastic model of one-dimensional gas. At time zero, the gas consists of n identical particles that are randomly distributed on the real line and have zero initial speeds. Particles begin to move under the forces of mutual attraction. When particles collide, they stick together forming a new particle, called cluster, whose mass and speed are defined by the laws of conservation.
We are interested in the asymptotic behavior of Kn(t) as n→∞, where Kn(t) denotes the number of clusters at time t in the system with n initial particles. Our main result is a functional limit theorem for Kn(t). Its proof is based on the discovered localization property of the aggregation process, which states that the behavior of each particle is essentially defined by the motion of neighbor particles.
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Keywords: Sticky particles; particle systems; gravitating particles; number of clusters; aggregation; adhesion
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aoap/1211819793
Digital Object Identifier: doi:10.1214/07-AAP481
Mathematical Reviews number (MathSciNet): MR2418237
Zentralblatt MATH identifier: 1141.60068
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