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FOURIER ANALYSIS AND THE KINETIC THEORY OF GASES

Part of: Harmonic analysis in one variable Limit theorems Infinite-dimensional Hamiltonian systems

Published online by Cambridge University Press:  16 December 2011

József Beck
József Beck*
Affiliation:
Mathematics Department, Rutgers University New Brunswick, New Jersey, U.S.A. (email: jbeck@math.rutgers.edu)
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Abstract

In the so-called Bernoulli model of the kinetic theory of gases, where (1) the particles are dimensionless points, (2) they are contained in a cube container, (3) no attractive or exterior force is acting on them, (4) there is no collision between the particles, (5) the collisions against the walls of the container are according to the law of elastic collision, we deduce from Newtonian mechanics two basic probabilistic limit laws about particle-counting. The first one is a global central limit theorem, and the second one is a local Poisson law. The key fact is that we can prove the “realistic limit”: first the time interval is fixed and the number of particles tends to infinity (where the density particle/volume remains a fixed constant), and then, in the second step, the time tends to infinity.

MSC classification

Secondary: 37K99: None of the above, but in this section 42A99: None of the above, but in this section 60F05: Central limit and other weak theorems
Type
Research Article
Information
Mathematika , Volume 58 , Issue 1 , January 2012 , pp. 93 - 208
Copyright
Copyright © University College London 2012

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