Annals of Applied Probability

Clustering in a stochastic model of one-dimensional gas

Vladislav V. Vysotsky

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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.

Article information

Ann. Appl. Probab., Volume 18, Number 3 (2008), 1026-1058.

First available in Project Euclid: 26 May 2008

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Zentralblatt MATH identifier

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 82C22: Interacting particle systems [See also 60K35]
Secondary: 60F17: Functional limit theorems; invariance principles 70F99: None of the above, but in this section

Sticky particles particle systems gravitating particles number of clusters aggregation adhesion


Vysotsky, Vladislav V. Clustering in a stochastic model of one-dimensional gas. Ann. Appl. Probab. 18 (2008), no. 3, 1026--1058. doi:10.1214/07-AAP481.

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