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Comparison of modes of convergence in a particle system related to the Boltzmann equation
Linköping University, Department of Mathematics, Mathematical Statistics .
2010 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
Abstract [en]

The distribution of particles in a rarefied gas in a vessel can be described by the Boltzmann equation. As an approximation of the solution to this equation, Caprino, Pulvirenti and Wagner [3] constructed a random N-particle system.

In the equilibrium case, they prove in [3] that the L1-distance between the density function of k particles in the N-particle process and the k-fold product of the solution to the stationary Boltzmann equation is of order 1/N. They do this in order to show that the N-particle system converges to the system described by the stationary Boltzmann equation as the number of particles tends to infinity.

This is different from the standard approach of describing convergence of an N-particle system. Usually, convergence in distribution of random measures or weak convergence of measures over the space of probability measures is used. The purpose of the present thesis is to compare different modes of convergence of the N-particle system as N tends to infinity assuming stationarity.

Place, publisher, year, edition, pages
2010. , 55 p.
Keyword [en]
Random measures, Stochastic particle systems, The Boltzmann equation
National Category
Probability Theory and Statistics
URN: urn:nbn:se:liu:diva-61303ISRN: LiTH-MAT-EX--10/27--SEOAI: diva2:383583
Physics, Chemistry, Mathematics
Available from: 2011-02-03 Created: 2010-11-11 Last updated: 2011-02-03Bibliographically approved

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