The Motion of a Distinguished Particle in an Infinite Particle System.
STANFORD UNIV CALIF DEPT OF OPERATIONS RESEARCH
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At time zero the positions of atoms on the real line form a Poisson process. Each atom has mass one and travels with a random but constant velocity on the line independent of the other atoms. At time zero a distinguished particle is placed at the origin. Its motion is caused by collisions with the atoms. An atom is removed from the system when it collides with the particle. The joint distribution of the mass and velocity of the particle after a collision with an atom may depend on the mass and velocity of the colliding atom and the mass and velocity of the particle before collision. The random counting measure induced by the positions and velocities at the time of the particles nth collision of those atoms that have not yet collided with the particle has the same probability law as that of the random measure induced by the positions and velocities of all the atoms at time zero. It then follows that the mass-velocity process of the particle is a regular step Markov process and its transition function is computed. Author Modified Abstract
- Physical Chemistry
- Operations Research