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Stability of one-dimensional systems of colliding particles

Published online by Cambridge University Press:  14 July 2016

Alan F. Karr
Alan F. Karr*
Affiliation:
The Johns Hopkins University
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Abstract

Envision a one-dimensional system of infinitely many identical particles, in which initial particle positions constitute a Poisson random measure and the initial velocity of a particle depends only on its initial position. Given its initial conditions the system evolves deterministically, by means of perfectly elastic collisions. In this note we derive conditions for continuity of the probability laws of the system and of the particle paths, as functions of the parameters of the initial conditions. These results have the physical interpretation of stability theorems.

Keywords

INFINITE PARTICLE SYSTEMCOLLISION MODELWEAK CONVERGENCEPOISSON RANDOM MEASURE
Type
Short Communications
Information
Journal of Applied Probability , Volume 13 , Issue 1 , March 1976 , pp. 155 - 158
Copyright
Copyright © Applied Probability Trust 1976 

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References

Billingsley, P. (1965) Convergence of Probability Measures . Wiley, New York.Google Scholar
Harris, T. (1965) Diffusion with ‘collisions’ between particles. J. Appl. Prob. 2, 323–338.Google Scholar
Kallenberg, O. (1973) Characterization and convergence of random measures and point processes. Z. Warscheinlichkeitsth. 27, 9–21.CrossRefGoogle Scholar
Karr, A. (1973) Weak Convergence Theorems for Some Infinite Particle Systems. Ph.D. dissertation, Northwestern University.Google Scholar